The angle of elevation to the top of a television towe is 45°from each of the two points on the ground level with its base.the point 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

Let's denote the height of the tower as h and the distance from the tower to the point due south as x.

From the given information, we can create a right triangle with the tower, the point directly south of the tower, and the top of the tower. The angle of elevation from the point south is 45°, so we have:

tan(45°) = h/x
1 = h/x
h = x

Now, we can create another right triangle with the tower, the point due east, and the top of the tower. Since the two points are 60 cm apart, the distance from the point due east to the tower is also 60 cm. We can label this distance as y.

Using the same reasoning as above:

tan(45°) = h/y
1 = h/y
h = y

Since the two points are 60 cm apart, x + y = 60. Since h = x and h = y, we have:

2h = 60
h = 30

Therefore, the height of the tower is 30 cm.