Question

30. Find the angle of depression from the top of a lighthouse 275 feet above water to a boat 1,324 feet

off shore.

Answer 1

Answer:

Angle of depression is 78.27°

Step-by-step explanation:

The height of the light house = 275ft

Distance of the boat from the lighthouse = 1,324ft

The angle of depression = ?

To solve this question, we'll require a well detailed diagram to illustrate how the light house makes angle with the boat.

See attached document for better illustration

Using SOHCAHTOA,

tanΘ = opposite / adjacent

Opposite = 1,324

Adjacent = 275

tanΘ = 1324 / 275

tanΘ = 4.8145

Θ = tan⁻4.8145

Θ = 78.266°

The angle of depression is 78.27°

Answer 2

The required angle of depression is $11.98^{\circ}$

Given that,

Perpendicular=275 feet

Hypotenues=1324 feet

The diagram is attached below,

Then,

$sinx=\frac{P}{H} \\=\frac{275}{1324} \\x=11.98^{\circ}$

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