Mr. Santos wanted to know the height of the tree. He observed from a point A that the angle of elevation of the top of the tree is 36 degrees. He then moved backwards 50 ft away from the initial point A, the angle of elevation of the top of the tree was 22 degrees. Find the height of the tree.
Answers
Answer:
The height of the tree is approximately 45.51 ft.
Step-by-step explanation:
The given information are;
The angle of elevation of the top of tree is 36 degrees
The distance backwards Mr. Santos moved = 50 ft.
The new angle of elevation of the top of the tree = 22 degrees
Therefore, we have;
The angle opposite to the 50 ft. side = 180 - (180 - 36) - 22° = 14°
Therefore, we have, by sine rule;
50/(sin(14)) = X/(sin(22))
X = (sin(22)) × 50/(sin(14)) ≈ 77.42 ft.
The height of the tree, T = X × sin(36°)
T = 77.42 ft. × sin(36°) ≈ 45.51 ft.
The height of the tree is approximately 45.51 ft
Related Questions
The area A of the rectangle shown
is described with the inequality
60 A 140. Write and solve a
compound inequality for x.
Answers
Step-by-step explanation:
Simplifying
4x + -5 = 20x
Reorder the terms:
-5 + 4x = 20x
Solving
-5 + 4x = 20x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-20x' to each side of the equation.
-5 + 4x + -20x = 20x + -20x
Combine like terms: 4x + -20x = -16x
-5 + -16x = 20x + -20x
Combine like terms: 20x + -20x = 0
-5 + -16x = 0
Add '5' to each side of the equation.
-5 + 5 + -16x = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -16x = 0 + 5
-16x = 0 + 5
Combine like terms: 0 + 5 = 5
-16x = 5
Divide each side by '-16'.
x = -0.3125
Simplifying
x = -0.3125
Write 5.77 x 10 in standard form.
5.77 x 10–2
Answers
Answer:
The answer is 57.7 x.
Step-by-step explanation:
100 POINTS!!!!!!!!!!! ( I NEED FAST ANSWERS ) Find the slope of the line that contains the points:(-6, 3) and (-4,5).
Answers
Answer:
slope = -4/5
Step-by-step explanation:
plllsssssssssss I needddd ansswwerss
Answers
Answer:
9/4 or 2¼
Step-by-step explanation:
have the number be represented by x2/3s OF x (of means to mulitply); 3 INCREASED BY (increased by means to add); 1/2 OF x (again, of means to multiply)so we can write the equation like this:2/3x=3+1/2xnow we need to get x by itselfmultiply both sides of the equation by 2/1 (the reciprocal of 1/22/3(2/1)=4/3 ; 1/2(2/1)=1now our equation look like 4/3x=3multiply both sides of the equation by 3/4 (the reciprocal of 4/3)4/3(3/4)=1 ; 3(3/4)=9/4x = 9/4 or 2¼Use the function to fill in the table.
g(x)=-3x+1
Answers
-16 - (-t) = -45 how do you solve this please help
Answers
Answer:
- 29
Step-by-step explanation:
Step 1:
- 16 - ( - t ) = - 45 Equation
Step 2:
- 16 + t = - 45 Open Parenthises
Step 3:
t = - 45 + 16 Add 16 on both siddes
Answer:
t = - 29
Hope This Helps :)
Answer:
t = -29
Step-by-step explanation:
Step 1: Write equation
-16 - (-t) = -45
Step 2: Solve for t
Simplify: -16 + t = -45Add 16 to both sides: t = -29Step 3: Check
Plug in t to verify it's a solution.
-16 - (-(-29)) = -45
-16 - 29 = -45
-45 = -45
Deb has two paintings in her portfolio
and paints three more each week. Kay has
twelve paintings in her portfolio and paints
two more each week. After how many
weeks will Deb and Kay have the same
number of paintings?
Answers
This is basically giving the equation of
3x + 2 = 2x + 12
You would subtract 2x from both sides, and 2 from both sides, and you would get x = 10
3.The snow starts at a depth of 10 inches and melts to 2 inches over the span of 4 hours. Determine the rate of change over the interval 0≤x≤4A.4 inches per hour
B.2 inches per hour
C.8 inches per hour
D.12 inch per hour
4.The population in a neighborhood increased from 120 to 156 people from 1990 to 1994. Find the rate of change over the interval 1990≤x≤1994.
A.1/9 of a person per year
B.9 people per year
C.36 people per year
D.4 people per year
5.The temperature increases from 60 degrees Fahrenheit to 84 degrees Fahrenheit from 8 in the morning to 12 in the afternoon. Find the rate of change over the interval 8≤x≤12
A.16 of a degree Fahrenheit per hour
B.4 degrees Fahrenheit per hour
C.6 degrees Fahrenheit per hour
D.24 degrees Fahrenheit per hour
If you answer, answer with all of the questions listed thank you.
Answers
3. B: 2 inches
4. C: 9 people
5. B: 6 degrees
dont answer this question i made it accidentally
Answers
HURRY!! THIS ASSIGNMENT IS DUE IN 5MIN!!! THANK YOU!!!!!!
Find the discounted price.
flashlight: $18.00 discount: 25%
Answers
Answer:
You can also calculate how much you save by simply moving the period in 25.00 percent two spaces to the left, and then multiply the result by $18 as follows: $18 x . 25 = $4.50 savings.
ANSWER ASAP!!!!! Evaluate ƒ(x) = |3x – 2| for ƒ(–5) and ƒ(7). Question 7 options: A) ƒ(–5) = 8, ƒ(7) = 7 B) ƒ(–5) = 12, ƒ(7) = –2 C) ƒ(–5) = –17, ƒ(7) = 9 D) ƒ(–5) = 17, ƒ(7) = 19
Answers
Answers:
f(-5) = 17f(7) = 19====================================
Work Shown:
Plug in x = -5. Use PEMDAS to simplify
f(x) = |3x-2|
f(-5) = |3(-5)-2| ... replace every x with -5
f(-5) = |-15-2|
f(-5) = |-17|
f(-5) = 17
---------------------
Repeat for x = 7
f(x) = |3x-2|
f(7) = |3*7-2| ... replace every x with 7
f(7) = |21-2|
f(7) = |19|
f(7) = 19
-5r - 10 = 10
HELP ASAP
Answers
Answer:
r equals -4
Step-by-step explanation:
there's your help
Cleo and jandi are having a Halloween party. They have 3 1/2 pounds of candy to divide into 14 goodie bags. How much candy will be in each bag?
Answers
Answer:
1/4 pound(s) of candy in each bag
Step-by-step explanation:
3 1/2 (pounds of candy) ÷ 14 (goodie bags) = ?
To make this easier let's turn 3 1/2 into a improper fraction and flip 14/1 (14/1 to 1/14):
3 1/2 = 7/2 14/1 = 1/14
Now we multiply:
7/2 x 1/14 = 7/28 = 1/4
(When you divide fractions, you can flip the second fraction and multiply and get your answer. Remember to simplify once you get your answer!)
Hope I helped! Sorry if wrong!
Answer:
1/4 pounds
Step-by-step explanation:
If 12 cats can catch 6 rats in 2 hours, how many hours would it take 50 cats to catch 75 rats?
Answers
Answer:
50 cats would take 6 hours to catch 75 rats.
Step-by-step explanation:
After reading the statement we noticed the existence of two relationships:
1) The amount of cats is directly proportional to the quantity of caught rats.
2) The amount of cats is inversely proportional to time taken to catch rats.
That is to say:
[tex]n \propto \frac{x}{y}[/tex]
[tex]n = k\cdot \frac{x}{y}[/tex] (Eq. 1)
Where:
[tex]n[/tex] - Amount of cats, dimensionless.
[tex]x[/tex] - Amount of caught rats, dimensionless.
[tex]y[/tex] - Time, measured in hours.
[tex]k[/tex] - Proportionality ratio, measured in hours.
Then, we obtain the following relationship by eliminating the proportionality ratio in (Eq. 1):
[tex]\frac{n_{1}\cdot y_{1}}{x_{1}} = \frac{n_{2}\cdot y_{2}}{x_{2}}[/tex] (Eq. 2)
Where:
[tex]n_{1}[/tex], [tex]n_{2}[/tex] - Initial and final amounts of cats, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final amounts of caught rats, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final times, measured in hours.
Now we clear final time in (Eq. 2):
[tex]y_{2} = y_{1}\cdot \left(\frac{n_{1}}{n_{2}} \right)\cdot \left(\frac{x_{2}}{x_{1}} \right)[/tex]
By knowing that [tex]y_{1} = 2\,h[/tex], [tex]n_{1} = 12[/tex], [tex]x_{1} = 6[/tex], [tex]n_{2} = 50[/tex], [tex]x_{2} = 75[/tex], then we get that time taken by 50 cats to catch 75 rats is:
[tex]y_{2} = (2\,h)\cdot \left(\frac{12}{50} \right)\cdot \left(\frac{75}{6}\right)[/tex]
[tex]y_{2} = 6\,h[/tex]
50 cats would take 6 hours to catch 75 rats.
find y when x=7 if y=3 when x=2
Please help
Answers
HOW TO SOLVE:
set 3/2 equal to x/7 and then solve for x. To do that, multiply 7x3 to get 21. Then divide 21 by 2 to get the answer.
A(x) = x² +10x - 75
rewrite in factored form
Answers
Step-by-step explanation:
A(x) = x² + 10x -75
= (x + 15)(x - 5)
Answer:
(x+15)(x-5)
Step-by-step explanation:
(5x² + 8x - 3) + (2x² - 7x + 13x)
Answers
Answer:
Simplify the expression.
7x2+14x−3
Step-by-step explanation:
The required simplification can be given as 7x²+ 14x - 3
What is simplification?
The operation in mathematics to process and interpret the relation to make function simple or more simple is called simplify and the phenomenon is called simplification.
We have,
= (5x² + 8x - 3) + (2x² - 7x + 13x)
= 5x²+ 2x²+ 8x - 7x + 13x - 3
= 7x²+ 14x - 3
Thus, the required simplification can be given as 7x²+ 14x - 3
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
someone please help me
Answers
Answer:
1/49 it is the equal to that
Step-by-step explanation:
I
What is the Next three term of this sequence 1,-3,-7,-11
Please help me
Answers
Answer:
-15, -19, -23
Step-by-step explanation:
Simply subtract 4 from the terms
Answer:
15 is the answer
Step-by-step explanation:
16/7 - 1/14 subtracting fractions
Answers
Answer:
31/14
Step-by-step explanation:
We first need to get common denominators, so we multiply the 16 and the 7 by 2, to get 32/12. Now we can subtract since the fractions have common denominators. After subtracting we get 31/14 or 2 3/14. Hope this helps!
9. PRODUCTION Brown Pencil factory can
produce 150 gross of pencils in a quarter of an
hour. At this rate, how many gross of pencils
can the factory produce in seven and a half
hours?
Please hurry
Answers
Answer:
4500
Step-by-step explanation:
d=b^2-4ac solve for a
Answers
Answer:
a=-d/4c+b^2/4c
Step-by-step explanation:
khan academy graph from the linear standard form.
Graph -14x + 21y = 84
Answers
Answer:
16
Step-by-step explanation:
because i am smort
rewrite the expression from part B using the additive inverse that you identified in part C.
Answers
Answer:
12.3 – (-9.6) = 12.3 + 9.6
Step-by-step explanation:
The ratio of boys to girls on the cross country team is 5 to 3. How many girls are on the team if there are 25 boys on the cross country team?
Answers
Answer:
If there are 25 boys on the team, we need to find out what 25 divided by 5 is.
It is 5.
So next wed o 5x3.
That's 15.
So there are 15 girls on the team.
Hope this helps!
Answer:
the answer is 15.
Step-by-step explanation:
5x5 = 25 so you would multiply 3x5 to get 15.
cuantos años tengo 33-45+62
Answers
Answer:
tienes 50 años
Step-by-step explanation:
PEMDAS
33-45+62
45+62=107
107-33=50
PLS HELP! WILL BE MARKING BRAINLIEST!!!!!!!!
Answers
Answer:
Tracy most likely saw 13 cars, and 13 motorcycles. Other solutions that you can find are: average number of tires in the area, the mode number of tires in the area (see the most often), etc.
Step-by-step explanation:
2x + 4x = 78
2(13) + 4(13) = 78
As 13 and 13 are two prime numbers, the answer will be 13.
Select the prime factors of 204.
A. 2 x 17
B. 6 x 17
C. 2 x 3 x 17
D. 2 x 2 x 3 x 17
Answers
A test tube is cylindrical in shape with a length of 152 mm and a radius of 6.5 mm. What is the volume of the test tube? Report your answer in mm3 but do not include the unit mm3 in your answer box. Round your answer to the nearest whole number and do not include commas in your answer. The formula for volume of a cylinder is V=πr2h.
Answers
Answer:
20165
Step-by-step explanation:
Given:
Length/height (h) of cylindrical test tube = 152 mm
Radius of cylindrical test tube = 6.5 mm
Volume = [tex] \pi r^2h [/tex]
Required:
Volume of cylinder to nearest whole number
Solution:
The volume is given as [tex] V = \pi r^2h [/tex]
Take π as 3.14 and plug the values of r and h into the volume formula.
[tex] V = 3.14*6.5^2*152 [/tex]
[tex] V = 3.14*6.5*152 = 20165.08 [/tex]
Volume of the test tube = 20165 mm³ (nearest whole number)
6(2x - 4) = 12w
solve for x
Answers
Answer:
x = w + 2
General Formulas and Concepts:
Order of Operations: BPEMDAS
Distributive Property
Step-by-step explanation:
Step 1: Write equation
6(2x - 4) = 12w
Step 2: Solve for x
Distribute 6: 12x - 24 = 12wSubtract 24 on both sides: 12x = 12w + 24Divide 12 on both sides: x = (12w + 24)/12Factor GCF: x = 12(w + 2)/12Simplify: x = w + 2