a Guard observes an enemy boat from an Absolution Tower at a height of 18 m above sea level at an angle of depression of 29 degree calculate to the nearest metre the distance between the boat and the foot of the observation Tower after sometime it is observed that the boat is 200 m from the foot of the observation Tower calculate the angle of depression
Answers
Answer:
First case, Boat is 24.4 meters away from foot of the tower.
Second case, So the angle of depression is 6 degrees.
Step-by-step explanation:
The angle of depression is angle made from horizontal surface to the line drawn below.
In the figure, ‘d’ is the angle of depression.
From top of tower, when you see the boat, it makes right angle triangle as shown.
Since d is angle of depression, 90 – d is the angle CAB in the right angle triangle ABC.
As d = 29 degees, Angle CAB = 90 – 29 = 61 degrees.
We need to find the distance of boat from foot of the tower = BC.
Tan(61 degrees) = BC / AB = BC / 18 (Tower height = 18 m)
1.8 = BC/18
Thus BC = 1.8 x 18 = 24.4m.
Boat is 24.4 meters away from foot of the tower.
In the second instance, BC = 200 meters.
Tan(Angle) = 200/18
Angle = Inverse Tan(200/18) ~ 84 degrees.
So the angle of depression is 90 – 84 = 6 degrees.
Answer:
Step-by-step explanation:boi