the angle of elevation and angle of depression of the top and base of a mobile tower from a mobile handset are 60degree and 30degree respectively. if the distances of the top and the bass of the tower from the mobile handset are 15metre and 8metre respectively, find from the height of the tower.
Draw a diagram and review your basic trig functions. It should be clear that the height is
15 sin60° + 8 sin30°
Cos 10°
To find the height of the tower, we can use trigonometric ratios such as tangent and sine.
Let's represent the height of the tower as 'h'.
From the given information, we know the following:
Angle of elevation (θ1) = 60 degrees
Angle of depression (θ2) = 30 degrees
Distance from the top of the tower to the mobile handset (d1) = 15 meters
Distance from the base of the tower to the mobile handset (d2) = 8 meters
Using the angle of elevation, we can define the tangent of the angle as the ratio of the opposite side (height of the tower) to the adjacent side (distance from the top of the tower to the mobile handset):
tan(θ1) = h / d1
Substituting the given values, we get:
tan(60 degrees) = h / 15 meters
Similarly, using the angle of depression, we can define the tangent of the angle as the ratio of the opposite side (height of the tower) to the adjacent side (distance from the base of the tower to the mobile handset):
tan(θ2) = h / d2
Substituting the given values, we get:
tan(30 degrees) = h / 8 meters
Now, using a scientific calculator, find the tangent values of 60 degrees and 30 degrees:
tan(60 degrees) ≈ 1.732
tan(30 degrees) ≈ 0.577
We can now solve the above equations for 'h':
1.732 ≈ h / 15
h ≈ 1.732 * 15
h ≈ 25.98 meters
0.577 ≈ h / 8
h ≈ 0.577 * 8
h ≈ 4.62 meters
Therefore, the height of the tower is approximately 25.98 meters from the top and 4.62 meters from the base.