Question

The elevation of the top of a tower of height 60m from two places on the same horizontal line due east of it are 60° and 45°. Find the distance between the two points.

A. 40 meters
B. 80 meters
C. 120 meters
D. 160 meters

Answer 1

The distance between the two points is 20(√3 - 1) meters.

Step-by-step explanation:

To find the distance between the two points, we can use trigonometric ratios and the concept of tangent.

Let x be the distance between the tower and the point where the angle of elevation is 45 degrees. Then, the height of the tower can be represented as x*tan(45) = x.

Similarly, let y be the distance between the tower and the point where the angle of elevation is 60 degrees. Then, the height of the tower can be represented as y*tan(60) = y*√3.

Since the height of the tower is given as 60 meters, we can set up the following equations:

x = 60

y*√3 = 60

From the second equation, we can solve for y: y = 60/√3 = 20√3.

Now, we can find the distance between the two points by subtracting x from y: 20√3 - 60 = 20√3 - 20√3 = 20√3 - 20 = 20(√3 - 1).

Therefore, the distance between the two points is 20(√3 - 1) meters.