Question

trig word problems (level 2)score: 1/3 penalty: nonequestiona boat heading out to sea starts out at point a, at a horizontal distance of 590 feet from a lighthouse/the shore. from that point, the boats crew measures the angle of elevation to the lighthouses beacon-light from that point to be 11°. at some later time, the crew measures the angle of elevation from point b to be 2°. find the distance from point a to point b.round your answer to the nearest foot if necessary.show examplesanswer attempt 2 out of 22696feetsubmit answer

Explanation:

Step1: Find lighthouse height

Let $h$ = lighthouse height. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$ for Point A.
$\tan(11^\circ)=\frac{h}{590}$
$h = 590\times\tan(11^\circ)$
$h\approx590\times0.1944=114.696$ feet

Step2: Find distance from B to shore

Use $\tan(2^\circ)=\frac{h}{d_B}$, solve for $d_B$.
$d_B=\frac{h}{\tan(2^\circ)}$
$d_B\approx\frac{114.696}{0.0349}\approx3286.42$ feet

Step3: Calculate distance AB

Subtract distance A from distance B.
$AB = d_B - 590$
$AB\approx3286.42 - 590=2696.42$

Answer:

2696 feet