Exercise 3 Page 877

A boat B is 310 feet from the base of a lighthouse A. The angle of depression from the top of the lighthouse C is 24^(∘). Let's analyze the given situation.

We are asked to find the height of the lighthouse AC to the nearest tenth of a foot. Since ∠ ACB is adjacent to 24^(∘), we get that m∠ ACB=90^(∘)-24^(∘)=66^(∘). Now, let's use the trigonometric ratios for right △ ABC.

cot(m∠ ACB)=AC/AB

SubstituteII

m∠ ACB= 66^(∘), AB= 310

cot 66^(∘)=AC/310

▼

Solve for AC

MultEqn

LHS * 310=RHS* 310

310cot 66^(∘)=AC

RearrangeEqn

Rearrange equation

AC=310cot 66^(∘)

UseCalc

Use a calculator

AC=138.020892...

RoundDec

Round to 1 decimal place(s)

AC≈ 138.0

Therefore, the height of the leighthouse is about 138 feet.