Question

The angle of depression from the top of a lighthouse to a boat in the water is 30°. If the lighthouse is 89 feet tall how far is the boat from the lighthouse to the nearest foot?

Answer 1

if ur doing usa test prep it’s B) 51 feet

Explanation:

Answer 2

The 51.39 feet far is the boat from the lighthouse .

Explanation:

Now by using the trignometric identity.

`cot\theta = (Base)/(Perpendicular)`

As given

The angle of depression from the top of a lighthouse to a boat in the water is 30°.

If the lighthouse is 89 feet tall .

As shown in the figure given below.

`\theta = 30^(\circ)`

Base = AC = 89 feet

Perpendicular = CB

Put in the identity .

`cot 30^(\circ) = (89)/(CB)`

`cot\ 30^(\circ) = 1.732`

Put in the above

`CB= (89)/(1.732)`

CB = 51.39 feet (Approx)

Therefore the 51.39 feet far is the boat from the lighthouse .