Question

a boat heading out to sea starts out at point a, at a horizontal distance of 815 feet from a lighthouse/the shore. from that point, the boats crew measures the angle of elevation to the lighthouses beacon-light to be $15^\circ$. at some later time, the crew measures the angle of elevation from point b to be $3^\circ$. find the distance from point a to point b. round your answer to the nearest tenth of a foot if necessary.
answer attempt 1 out of 2
feet submit answer

Explanation:

Step1: Find lighthouse height $h$

Use $\tan(15^\circ)=\frac{h}{815}$, so $h=815\times\tan(15^\circ)$
$h=815\times0.2679\approx218.34$ feet

Step2: Find distance $BL$

Use $\tan(3^\circ)=\frac{h}{BL}$, so $BL=\frac{h}{\tan(3^\circ)}$
$BL=\frac{218.34}{0.0524}\approx4165.9$ feet

Step3: Calculate distance $AB$

$AB=BL-AL$
$AB=4165.9-815=2996.9$ feet

Answer:

2996.9 feet