Question

At a certain point, the angle of elevation of a tower is found to be such that its cotangent is 13/5; on walking 32 m directly towards the tower its angle of elevation is an angle whose cotangent is 12/5. Then the height of the tower in meters is:

(a) 39
(b) 45
(c) 52
(d) 60

Answer 1

To find the height of the tower, set up two right triangles using the given cotangents. Calculate the height of each triangle and then find the difference to determine the height of the tower. The height of the tower is 60 meters.

Step-by-step explanation:

To find the height of the tower, let's assume the height of the tower is h meters. We can set up two right triangles, one before the person walks towards the tower and another after. The first triangle has a cotangent of 13/5, which means that the tangent is 5/13. Using the tangent, we can find the height of the first triangle using the equation h/32 = 5/13. Solving for h, we get h = 160/13 meters.

In the second triangle, the cotangent is 12/5, which means the tangent is 5/12. The base of the second triangle is 32 meters (the person walked towards the tower). Using the tangent, we can find the height of the second triangle using the equation (h -32)/32 = 5/12. Solving for h, we get h = 260/12 meters.

The height of the tower is the difference between the heights of the two triangles. So, the height of the tower is (260/12) - (160/13) = (1080/39) meters. Simplifying this, we get h = 60 meters. Therefore, the height of the tower is 60 meters.