Question

B) The angle of depression from an observation tower to boat A is 28 degrees. The angle of depression from the same point of the tower to boat B is 45 degrees. If the tower is 60 meters tall, approximately how far is boat A from boat B.

Answer 1

Answer:

53 meters

Step-by-step explanation:

The angle between a viewer's horizontal line of sight and the line of sight down towards a particle is called the angle of depression. For example if a viewer is sitting at the top of a tower and looking down on a car, the angle between the viewer's horizontal line of sight and the line of sight to which he looks at the car is the angle of depression.

A sketch of the positions of the boats and the tower has been attached to this response.

As shown,

the distance between the two boats A and B is marked x meters.

the horizontal distance between boat A and the foot of the tower is y meters.

the horizontal distance between boat A and the foot of the tower is  x + y meters.

the height of the tower is 60 meters.

the angle of depression of boat A is 28°

the angle of depression of boat B is 45°

To find the value of y, from triangle DBC we use the trigonometric ratio for tangent. i.e

tan 45° = $\frac{60}{y}$

1 = $\frac{60}{y}$

y = 60 meters

To find the value of x, from triangle ABC we use the trigonometric ratio for tangent. i.e

tan 28° = $\frac{60}{x+y}$

Where y = 60 meters

tan 28° = $\frac{60}{x+60}$

0.5317 = $\frac{60}{x+60}$

x + 60 = $\frac{60}{0.5317}$

x + 60 = 112.85

x = 112.85 - 60

x = 52.85 meters

Therefore, boat A is about 53 meters from boat B