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° = [tex]\frac{60}{y}[/tex]
1 = [tex]\frac{60}{y}[/tex]
y = 60 meters
To find the value of x, from triangle ABC we use the trigonometric ratio for tangent. i.e
tan 28° = [tex]\frac{60}{x+y}[/tex]
Where y = 60 meters
tan 28° = [tex]\frac{60}{x+60}[/tex]
0.5317 = [tex]\frac{60}{x+60}[/tex]
x + 60 = [tex]\frac{60}{0.5317}[/tex]
x + 60 = 112.85
x = 112.85 - 60
x = 52.85 meters
Therefore, boat A is about 53 meters from boat B
