A man standing on a lighthouse at a height of 124 feet sights two boats directly in front of him. One is at an angle of depression of 62°, and the other is at an angle of depression of 33°. Identify the distance between the two boats. Round your answer to the nearest foot.

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calculista calculista · Answer 1 · 2019-03-25T03:10:50+01:00

Answer:

[tex]125\ ft[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ABC find the length side BC

we know that

[tex]tan(62\°)=\frac{124}{BC}[/tex]

[tex]BC=\frac{124}{tan(62\°)}[/tex]

step 2

In the right triangle ABD find the length side BD

we know that

[tex]tan(33\°)=\frac{124}{BD}[/tex]

[tex]BD=\frac{124}{tan(33\°)}[/tex]

step 3

we know that

The distance between the two boats is the length side CD

[tex]CD=BD-BC[/tex]

substitute the values

[tex]CD=\frac{124}{tan(33\°)}-\frac{124}{tan(62\°)}=125\ ft[/tex]