Consider the right triangle shown.
What is the length of the other leg?
Round your answer to the nearest tenth

Consider The Right Triangle Shown.What Is The Length Of The Other Leg?Round Your Answer To The Nearest

Answers

Answer 1
Basic Trigonometric Ratios

These are the three basic trigonometric ratios:

The sine ratio: [tex]\sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]The cosine ratio: [tex]\cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]The rangent ratio: [tex]\tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

Here, 'opposite' or adjacent are referring to the legs in relation to one of the interior angles of the triangle, θ.

We can use these ratios to help us solve for side lengths or angles, depending on what information is given to us and what information we must solve for.

Solving the Question

We're given:

The indicated angle (θ) measures 70° The adjacent side measures 5.7 unitsWe must solve for the other leg, which is the 'opposite' side

Because this question involves the adjacent and the opposite, we can use the tangent ratio to find the answer.

[tex]\tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

⇒ Plug in the given information:

[tex]\tan(70^\circ)=\dfrac{opposite}{5.7}[/tex]

⇒ Multiply both sides by 5.7 to isolate 'opposite:

[tex]5.7\tan(70^\circ)=opposite\\opposite = 15.66062\dots[/tex]

⇒ Round to the nearest tenth:

[tex]opposite=15.7[/tex]

Answer

The length of the other leg is 15.7 units.


Related Questions

HELP I WILL MARK BRAINLIEST TO WHOEVER ANSWERS CORECCTLY HELPP
liam earned $11.50 for each lawn mowed. he has a total of $81.77 after spending $10.23 on regular maintenance. write an equation to find how many lawns liam mowed

Answers

Answer:

11.50x - $10.23 = $81.77

Step-by-step explanation:

$11.50 is how much he made per hour and X is the number of lawns he mowed, but we don't know exactly how many.

$11.50x tells us how much money he made.

He spent some of that money, $10.23, on maintenance so

$11.50x - $10.23 he spent = $81.77 which is the amount of money they said he has left

Suppose that you need to build as many chairs as possible. Each chair requires one seat, one back, and four legs. If you have 12 seats, 15 backs, and 44 legs, which of the chair components limits the number of chairs you can make?.

Answers

Answer:

  legs limit the number of chairs that can be built

Step-by-step explanation:

The maximum number of chairs that can be built will be the minimum of the number of parts divided by the number of parts needed for each chair, as computed across the different kinds of parts required.

  seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible

  backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible

  legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible

The maximum number of chairs that can be built will be the minimum of 12, 15, and 11. That is, 11 chairs can be built, limited by the number of available legs.

The distance from one corner of a standard piece of paper to the diagonally opposite corner is 13.9 inches. If a piece of paper is 11 inches long, how many inches wide is it?

Answers

The width of the piece of paper as described in the task content is; 8.5in.

How wide is the piece of paper?

It follows from the task content that the diagonal of the rectangular piece of paper is 13.9in and the length of the piece of paper is; 11in long.

On this note, it follows from Pythagoras theorem that the width of the piece of paper is;

width = √(13.9² - 11²)

Width = √72.21

Width = 8.5in

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Roger bought a hamburger and french fries for $4.84. He paid with a $10 bill. Abouthow much change should he have gotten back?

Answers

Answer:

Roger should get $5.16 back.

Step-by-step explanation:

Just do $10.00 - 4.84

Answer:

$ 5.16

Step-by-step explanation:

10.00 - 4.84 = 5.16

PLEASE HELP ASAP! WILL GIVE BRAINLIEST! (Please complete both)

Answers

Answer:

A: 5 cm2

B: 9 3/8 cm2

Step-by-step explanation:

Question A:

4 x 1 1/4

4/1 x 5/4 = 20/4

20/4 = 5 cm2

Question B:

3 3/4 x 2 1/2

15/4 x 5/2 = 75/8

75/8 = 9 3/8 cm2

Mrs. franklin has a rectangular piece of fabric with an area of 198 square inches it is 9 inches wide how long is the piece of fabric

Answers

Answer:

22 inches

Step-by-step explanation:

Area = length x width

198 / 9 = l

22 = l

Please help, asap, 50 points!

Answers

Answer:

k = 30/1

The constant of proportionality is 30:1. If we divided the number of area to be covered and the number of scoops, we will always get 30. 60/2 is 30, 120/4 is 30. 180/6 and 240/8 all equal 30.

Step-by-step explanation:

What is the y-value of the solution to the system of equations? 3x 5y = 1 7x 4y = −13 −3 −1 2 5

Answers

The y-value of the solution to the system of equations is 2.

We have given a system of equation

3x + 5y = 1

7x + 4y = −13

What is the system of equation?

A system of equations is a collection of two or more equations with the same set of unknowns.

First we have to find the value of x.

3x + 5y - 5y = 1 - 5y

divide both sides of the equation by 3

3x/3 = 1/3 - 5y/3

x = 1/3 - 5/3y

Now plug that into the other equation,

7(1/3 - 5/3y) + 4y = -13

7/3 - 35/3y + 4y = -13

7/3 - 7 2/3y - 7/3 = -13 - 7/3

- 7 2/3y (-3/23) = -15 1/3 (-3/23)

y = 2

The answer is 2.

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Compare.
160 seconds
minutes 2 1/2

Answers

Answer:

160 is greater than 2 and a half minutes.

Step-by-step explanation:

Use a calculator to solve each problem. Round your answers to the nearest hundredth.

What is the absolute magnitude of a star that has a period of 62 days?

Answers

Answer:-6.33

Step-by-step explanation:

its correct, i did it on a test

Give the degree of the polynomial.
4
u v + 3y'wu^ +6w+ + 6

Answers

Answer:

12 is the polynomial degree

A line passes through (-5,2) and has a slope of -1. What is an equation of the line in slope-intercept form?

A. y+2=-(x-5)

B. y=-x-3

C. y-2=-(x+5)

D. y=-x+3​

Answers

Answer:

B. y=-x-3

Step-by-step explanation:

[tex]f(x) = ax + b \\ a = - 1 \\ (x \: y) = ( - 5 \: \: 2) \\ f( - 5) = - ( - 5) + b = 2 \\ 5 + b = 2 \\ b = - 3 \\[/tex]

So,

[tex]f(x) = - x - 3 \\ y = - x - 3[/tex]

Hope it helps

Equation in point slope form

y-y1=m(x-x1)y-2=-1(x+5)y-2=-x-5y=-x-3

Math help!!!!!!!!!!!111

Answers

Answer:

it would be 3 8/10

Step-by-step explanation:

you have to find a common multiple and it would be 10 thin you add them up 7/10+1/10=8/10 plus you have to put the 3 with the 8/10

1,030 at 4% compounded semiannually for 2 years

Answers

Answer: $1114.91

Step-by-step explanation:

The formula for compound interest is

[tex]A= P(1+\frac{r}{n})^{nt} \\[/tex]

Where

A = final amount

P = initial principal balance (1030 for this)

r = interest rate (0.04 for this)

n = number of times interest applied per time period (2 for this)

t = number of time periods elapsed (2 for this)

[tex]A= 1030(1+\frac{.04}{2})^{(2)(2)} \\\\A= 1030(1+0.02)^{4} \\A=1030(1.02)^4\\A=1114.905125[/tex]

This rounds up to $1114.91

Find the lateral area of the cone

Answers

Answer:

Lateral surface area of the cone is 1005 cm²

Step-by-step explanation:

Given :-

Radius of cone = 16 cmHeight of cone = 12 cm

To Find :-

Lateral surface area

Solution :-

As we know that,

LSA of the cone = πrl

Finding Slant height:

➝ L = √r² + h²

➝ L = √(16)² + (12)²

➝ L = √256 + 144

➝ L = √400

➝ L = 20 cm

Slant height of cone is 20cm

Now,

LSA of the cone = πrl

Substituting the required values,

➝ LSA = 22/7 × 16 × 20

➝ LSA= 7040/7

➝ LSA ≈ 1005 cm²

Hence,

Lateral surface area the of cone is 1005 cm²

The first three terms of a sequence are given. round to the nearest thousandth (If necessary). 15,18,108/5 Find the 7th term pls help

Answers

The sequence 15, 18, 108/5 is a geometric sequence

The value of the 7th term is [tex]44\frac{2468}{3125}[/tex]

How to determine the 7th term?

The sequence is given as:

15, 18, 108/5

The above sequence is a geometric sequence with the following parameters:

First term, a = 15

Common ratio = 18/15

The nth term of a geometric sequence is:

an = a * r^(n - 1)

So, the 7th term is:

a7 = a * r^6

This gives

a7 = 15 * (18/15)^6

Evaluate

[tex]a_7 = 44\frac{2468}{3125}[/tex]

Hence, the value of the 7th term is [tex]44\frac{2468}{3125}[/tex]

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PLEASE help me. This is honestly super confusing and I would love it if someone answered it. Also, please explain your answer as well. Thank you :)

Answers

Check the picture below.

so the wall is 146 inches wide, half of that is 73 inches.

the painting is 30 and 1/2 inches wide, half that is 15 and 1/4 inches.

if we subtract half the width of the painting from half the wall's width, the center of the painting will match the center of the wall.

[tex]73~~ - ~~15\frac{1}{4}\implies 73~~ - ~~\cfrac{61}{4}\implies \cfrac{292~~ - ~~61}{4}\implies \cfrac{231}{4}\implies 57\frac{3}{4}[/tex]

question #10. The question is in the picture. I'd like a bit of help, please. I will give 15 points to whoever can help out.

Answers

the answer would be C.

A city doubles its size every 24 years. If the population is currently 145,000, what will the population be in 48 years?

Answers

Answer:

145000x2

=answer

then

answer×2

= final answer

Answer:

580,000 people

Step-by-step explanation:

First, find out how many times the population will double. Divide the number of years by how long it takes for the population to double.

48÷24=2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

145,00022=580,000

That calculation could also be written with exponents:

145,000 x 2^2=580,000

After 48 years, the population will be 580,000 people.

5 STARS ON YOUR ACCOUNT!!! AND COMMENTS AND A THANK YOU

Answers

Essentially, we want to find the number of ounces of dough she used to measure:

   ⇒ which means that we must convert the:

      ⇒ grams of dough to ounces of dough

        ⇒ 28.6 grams  = 1 oz

Essentially,we can set up a proportion:

    ⇒ 28.6 grams to 1 oz

        ⇒ is to 200.2 grams to 'x' oz

  (mathematically)

   [tex]\frac{28.6}{200}=\frac{1}{x} \\28.6x = 2000\\x = 6.99[/tex]

Thus 200.2 grams is to 7 oz (rounded)

Answer: 7 ounces

Hope that helps!

A newspaper printer can print 15,000 newspapers in 4 hours. At the same rate, how many newspapers can they print in 24 hours?

Answers

Answer: its gonna be 90k (90,000)

Step-by-step explanation: 4 hrs = 15k meaning if u add 4 + 4 its basically gonna be 15k + 15k. so in 24 hr its gonna be 90k because 4 + 4 + 4 +4 + 4 = 24 so if 4 is 15k then it would also be 15k + 15k + 15k +15k +15k and thats 90k.

i took the test. and give brainliest pls

HCF of 77,91 and 143 using division method​

Answers

1

hope it helps....!!!!!

2. Which theorem can you use to conclude that AABC ~ ADEF?

A. the pythagorean theorem
B. triangle sum theorem
C. angle-angle similarity theorem
D. interior angle theorem

Answers

Answer:

A

Step-by-step explanation:

i had the same question when i had honors trust me :> you gut this

The circumference of a circle is 15.03
m. Find the radius and round to the
nearest hundredth.

Answers

Answer:

2.39 meters

Step-by-step explanation:

Given:

Circumference = 15.03 meters

Circumference:

[tex]\displaystyle \large{C=2\pi r}[/tex]

C = circumference = 15.03r = radius

Therefore:

[tex]\displaystyle \large{15.03=2\pi r}[/tex]

Divide both sides by 2π:

[tex]\displaystyle \large{\dfrac{15.03}{2\pi}=\dfrac{2\pi r}{2\pi}}\\\displaystyle \large{2.3920... = r}[/tex]

Round to nearest hundredth:

[tex]\displaystyle \large{r=2.39}[/tex]

Therefore, the radius is 2.39 meters

How many degrees is the angle measurement of​

Answers

Answer:

x° = 37.13°

Step-by-step explanation:

13.4 = cathetus opposite the angle "x°"

22.4 = hypotenuse

[tex]sin(x^{o}) =\frac{13.4}{22.2}=0.6036[/tex]

[tex]x^{o} =sin^{-1} (0.6036)=37.13^{o}[/tex]

Hope this helps

The distribution of z-scores is always Group of answer choices the same shape as the distribution of raw scores. positively skewed. negatively skewed. more spread out than the distribution of raw scores.

Answers

The true statement about the distribution of the z score is that they have (a) same shape as the distribution of raw scores.

How to determine the true statement?

The z score of a dataset is calculated using:

z = (x - μ)/σ

Where

x represents the raw scoreμ represents the meanσ represents the standard deviation

The above formula implies that the z-scores are derived from the raw scores, and so they would have the same shape as the raw score

Hence, the true statement is (a) same shape as the distribution of raw scores.

Read more about z-scores at:

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50 POINTS PLEASE HELP Layla has a bag that contains orange chews, lemon chews, and lime chews. She performs an experiment. Layla randomly removes a chew from the bag, records the result, and returns the chew to the bag. Layla performs the experiment 71 times. The results are shown below:
A orange chew was selected 11 times.
A lemon chew was selected 18 times.
A lime chew was selected 42 times.

If the experiment is repeated 100 more times, about how many times would you expect Layla to remove a lemon chew from the bag? Round your answer to the nearest whole number.

Answers

Answer:Orange 11/71 , lemon 18/71 , lime 42/71

2. Answer is 25

Step-by-step explanation: The answers above correlate with an independent situation where Leyland always replaced the fruits.

Orange :lemon;lime is 11:18:42

In 100 Selections, lemon will be 18/71×100/1 =25.35

Answer:

25

Step-by-step explanation:

shawnye drinks 1/2 of 6-ounces glass of water in 2/3 hours how much water dose she drink in 1 hour.

Answers

Answer:

She drinks 4.5 oz in 1 hour.

Step-by-step explanation:

First,

1/2 of 6 would be 3

Shawnte drinks 3 ounces of water in 2/3 hrs.

3 oz = 2 / 3 hr

Multiply both sides by 3 to get 2 alone.

3*(3 oz) = 3*(2/3 hr)

9 oz = 2 hrs

She drinks 9 ounces of water in 2 hours.

9 / 2 oz = 2 / 2 hrs

Divide both sides by 2 so you can get how much she drinks in one hours

4.5 oz = 1 hr

An easier way of doing this is dividing both sides by (2/3)3 oz = 2/3 hrsDivide both sides by 2/34.5 oz = 1 hrsAnd boom

f(x): x^2+1

g(x) = 5-x

(f + g)(x) =

1. X^2 + x - 4
2. X^2 + x +4
3. X^2-x + 6
4. X^2 + x + 6

thank you!

Answers

Answer:

f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ). Solution. Step 1. Find ( f – g ) ( x ). ( f – g ) ( x ) = f ...

Step-by-step explanation:

Find the mean, median, and mode of the data with and without the outlier. 85, 77, 211, 88, 91, 84, 85

Answers

Answer:

With Outlier:

Median: 85
Mean: 103
Mode: 85

Without Outlier:
Median: 85
Mean: 85
Mode: 85

Step-by-step explanation:

Basically order the numbers from least to greatest. Include the outlier to find the median, mean, and mode. The median is clear as day with the outlier, being the middlemost number: 77, 84, 85, 85, 88, 91, 211. To find the mean, just add all of the numbers together and then divide them by how many numbers there are. In this case, that'd be 7 and you get 103. The mode is simple as it's the number that repeats the most, which is basically 85 since it repeats twice in the set. After you find the median, mean, and mode with the outlier, now rewrite the numbers (still least to greatest) but excluding the outlier (211). It should now be 77, 84, 85, 85, 88, 91. For the median, our middlemost numbers are 85 and 85, so simply just add them together and then divide by two. This gets you 85 for the median. For the mean, simply just add the numbers in the new set excluding the outlier and divide by 6 since that's how many numbers we have in the set now. This gives you 85. The mode is the number most repeated, and that's still 85.

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