Question

a boat is heading towards a lighthouse, whose beacon-light is 129 feet above the water. from point a, the boats crew measures the angle of elevation to the beacon, $8^\circ$, before they draw closer. they measure the angle of elevation a second time from point b to be $13^\circ$. find the distance from point a to point b. round your answer to the nearest foot if necessary.
answer attempt 1 out of 2
feet
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Explanation:

Step1: Find distance AL (tan formula)

Let $AL$ = horizontal distance from A to lighthouse base L.
$\tan(8^\circ) = \frac{129}{AL}$
$AL = \frac{129}{\tan(8^\circ)}$
Calculate: $AL \approx \frac{129}{0.1405} \approx 918.15$ feet

Step2: Find distance BL (tan formula)

Let $BL$ = horizontal distance from B to lighthouse base L.
$\tan(13^\circ) = \frac{129}{BL}$
$BL = \frac{129}{\tan(13^\circ)}$
Calculate: $BL \approx \frac{129}{0.2309} \approx 558.70$ feet

Step3: Compute distance AB

$AB = AL - BL$
$AB \approx 918.15 - 558.70$

Answer:

359 feet