The angle of elevation to the top of a television tower is 45 degrees from each of the two points on the ground level with its base. The points are 60cm apart and one is due south and the other due east of the tower. What is the height of the tower?

Answer 1

To solve this problem, we can first draw a right triangle with the tower as the vertical side, the distance between the two points on the ground as the horizontal side, and the line from each point on the ground to the top of the tower as the hypotenuse.

Since the angle of elevation to the top of the tower is 45 degrees from both points on the ground, we have two right triangles that are both 45-45-90 triangles.

Let h be the height of the tower. The distance between the two points on the ground is 60cm, so the length of the hypotenuse (from each point to the top of the tower) in each triangle would be 60cm.

Now, we can use the properties of a 45-45-90 triangle to find the height of the tower. In a 45-45-90 triangle, the ratio of the sides is 1:1:√2.

Since the hypotenuse is 60cm, the height of the tower, which is the shorter leg of the triangle, would be:
h = 60cm / √2
h = 60cm / 1.414
h ≈ 42.43cm

Therefore, the height of the television tower is approximately 42.43cm.