A ladder 16 feet long leans against the side of a house. Find the height h from the top of the ladder to the ground when the angle of elevation of the ladder is 74°. Round your answer to the nearest tenth.
Answers
Answer:
15.38 feets
Step-by-step explanation:
Using Pythagoras rule :
Sinθ = opposite / hypotenus
Sin 74 = h / 16
0.9612616 = h / 16
h = 0.9612616 * 16
h = 15.38 feets
The sine ratio is the ratio of the height of the ladder to length of the
ladder.
Response:
The height from the top of the ladder to the ground is h ≈ 15.4 feetWhich method is used to find the height of the ladder?The length of the ladder = 16 feet
The angle of elevation of the ladder = 74°
Required:
The height of the top of the ladder from the ground, h
Solution:
By trigonometric ratios, we have;
[tex]sin(74^{\circ}) = \mathbf{ \dfrac{h}{16}}[/tex]
Therefore;
h = 16 feet × sin(74°) \approx 15.4 feet
The height h from the top of the ladder to the ground is approximately 15.4 feet.
Learn more about sine ratio here:
https://brainly.com/question/16173933
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Answer:
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Step-by-step explanation:
Given data
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Answer:
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Step-by-step explanation:
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At age 9, Gerald is 5 feet tall. If he grows at a rate of 1.5 inches per year, how old will he be when he hits 6 feet?
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Answer:
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Answer:
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answer:
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Malaya is standing directly between a 90 foot tall courthouse and a 54 foot tall bank. If the angle of elevation from Malaya to the top of the courthouse is 72° and the angle of elevation from Malaya to the top of the bank is 35°. What is the distance between the courthouse and the bank?
Answers
Answer:
the distance is about 106.36 feet
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What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
We are given that;
Height of court house= 90 foot
Height of bank= 54 foot
Now,
Use the tangent function to write two equations relating x, y, and the angles. For example:
tan(72°)=x90
tan(35°)=y54
Solve for x and y by multiplying both sides by x and y respectively. For example:
xtan(72°)=90
ytan(35°)=54
Divide both sides by tan(72°) and tan(35°) respectively to get x and y. For example:
x=tan(72°)90≈24.8
y=tan(35°)54≈77.9
Use the Pythagorean theorem to find z in terms of x and y. For example:
z2=x2+y2
Substitute the values of x and y and simplify to get z. For example:
z2=(24.8)2+(77.9)2
z2=615.04+6068.41
z2=6683.45
z=6683.45≈81.8
Therefore, by Pythagoras theorem the answer will be 81.8 feet.
Learn more about Pythagoras theorem;
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