Question

The angle of elevation from the top of a 45m tower from the foot of another tower is 60°, and the angle of elevation from the second tower to the foot of the first tower is 30°. Find the distance between the two towers and also find their heights.

a) Distance: 90m, Heights: 45m and 60m
b) Distance: 60m, Heights: 45m and 30m
c) Distance: 75m, Heights: 45m and 45m
d) Distance: 45m, Heights: 60m and 30m

Answer 1

The distance between the two towers is 127.5 m, and the heights of the towers are 45 m and 73.25 m, respectively. Option (a) is true.

Explanation:

From the diagram, we can see that we have two right triangles. We can use trigonometry to solve for the missing sides and angles.

In the first right triangle, we have:

Hypotenuse = 45 m (height of the first tower)

Angle of elevation = 60°

Adjacent side = x (distance between the towers)

We can use the tangent function to solve for x:

tan(60°) = x/45

Solving for x, we get:

x = 45 * tan(60°) ≈ 127.5 m

In the second right triangle, we have:

Hypotenuse = y (height of the second tower)

Angle of elevation = 30°

Adjacent side = 127.5 m (distance between the towers)

We can use the tangent function to solve for y:

tan(30°) = y/127.5

Solving for y, we get:

y = 127.5 * tan(30°) ≈ 73.25 m

Thus, option (a) is true.