Question

A boat is 40 meters away from a 33 meter tall lighthouse. What is the angle of depression (d1) from the top of the lighthouse to the boat? What is the angle of depression (d2) when the boat is 55 meters away from the lighthouse? Select all that apply.
d1 = 34°
d1 = 40°
d2 = 53°
d1 = 50°
d2 = 31°

Answer 1

Answer:

d1 = 40°  and d2= 31°

Step-by-step explanation:

Given: Height of light house = 33 m

To Find: 1]. Angle of depression (d1) from top of light house when

               boat is 40 m away.

             2]. Angle of depression (d2) from top of light house when

               boat is 55 m away.

Figure is attached. First boat at point C and then boat at point D

We know that angle of depression from top of lighthouse is equal to angle of elevation from boat.

using this result and trigonometric ratio, we get

In ΔABC

$tan\,C=\frac{AB}{CB}$

$tan\,C=\frac{33}{40}$

$tan\,C=0.825$

since, value of tan 40° = 0.825

⇒ m∠C = 40°

⇒ d1 = 40°

In ΔABD

$tan\,C=\frac{AB}{DB}$

$tan\,C=\frac{33}{55}$

$tan\,C=0.6$

since, value of tan 31° = 0.6

⇒ m∠C = 31°

⇒ d2 = 31°

Therefore, d1 = 40°  and d2= 31°