Question

a boat is 600 meters from the base of a cliff. Erika, who is sitting in the boat, notices that the angle of elevation to the top of the cliff is 32°. How high is the cliff?

Answer 1

Answer:

375 meters

Step-by-step explanation:

We use the tangent ratio to determine the height of the height of the cliff.

We have that, the boat is 600 meters from the base of a cliff.

We also know that, the angle of elevation to the top of the cliff is 32°

Using the tangent ratio, we have:

$\tan(32) = \frac{h}{600}$

We solve for h to obtain:

$600\tan(32) = h$

$h = 374.92$

Therefore the height of the cliff is approximately 375 meters

Answer 2

The angle of elevation is an angle that is formed between the horizontal line and the line of sight, hence the Height of the cliff is

374.4 meters

Height of Cliff/ Angle of Elevation

Given Data

Opposite/Height of cliff = ??

Adjacent/Distance of boat from base = 600 meters

Angle of elevation ∅  = 32°

By applying SOH CAT TOA

Tan  ∅ = Opp/Adj

Substituting our given Data we have

Tan 32 = Opp/600

0.624 = Opp/600

Cross multiply we have

Opp = 0.624*600

Opp = 374.4 meters

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