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From the top of a cliff 90 m high, the angle of depression of a boat on the sea is 26.2°. Calculate how far the boat is

a from the foot of the cliff,
b from the top of the cliff.​

User Hugo G
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1 Answer

10 votes
10 votes

Answer:

a) 182.90 m

b) 203.85 m

Explanation:

The relations between trig functions and measures in a right triangle are summarized in the mnemonic SOH CAH TOA. Here, we are given an angle and the side opposite, and we are asked to find the adjacent side and the hypotenuse.

__

a)

The foot of the cliff to the boat is the adjacent side of the angle in our model. So, we can use the relation ...

Tan = Opposite/Adjacent

Solving for the adjacent side, we have ...

BF = (90 m)/tan(26.2°) ≈ 182.90 m

The boat is about 182.90 meters from the foot of the cliff.

__

b)

The top of the cliff to the boat is the hypotenuse of the triangle we're using to model the situation. This means the applicable relation is ...

Sin = Opposite/Hypotenuse

BC = (90 m)/sin(26.2°) ≈ 203.85 m

The boat is about 203.85 meters from the top of the cliff.

From the top of a cliff 90 m high, the angle of depression of a boat on the sea is-example-1
User Mjsarfatti
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