Question

The angle of elevation to the top of a television tower is 45° from each of the two points on the ground level with it's base .The point are 60 centimeters apart and one is due south and the other due east of the tower .What is the height of the tower?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the height of the tower, we can create a right triangle with the tower as the vertical side, the ground as the horizontal side, and the line of sight from each point on the ground to the top of the tower as the hypotenuse.

Let's consider the triangle with one point due south of the tower. Since the angle of elevation is 45°, the angle at the top of the tower is also 45°, making it an isosceles right triangle. The distance from this point to the base of the tower is the base of the right triangle, which is 60 cm.

Using trigonometry, we can find the height of the tower using the tangent function:

tan(45°) = height of tower / 60 cm
1 = height of tower / 60 cm
height of tower = 60 cm

Therefore, the height of the tower is 60 cm.