Question

A tower stands on top of a hill. From a point on the ground that is 148 meters directly east of a point directly under the tower, the angle of elevation to the bottom of the tower is 18 degrees. From the same point, the angle of elevation to the top of the tower is 34 degrees. Find the height of the tower.

Answer 1

62.2 m

Explanation:

From 148m away at ground level, the angel of elevation to the tower base is 18 degrees. Imagining this as a right angled triangle, if considering the angle of 18 degrees, 148m is the adjacent and the opposite is the height of the hill:

tanA=opposite/adjacent

tan18=opposite/148

opposite = 57.8357059295m

From 148m away at ground level, the angel of elevation to the tower top is 34 degrees. Imagining this as a right angled triangle, if considering the angle of 34 degrees, 148m is the adjacent and the opposite is the height of the hill+the tower:

tanA=opposite/adjacent

tan34=opposite/148

opposite = 120.062515998m

Knowing the height of the hill and tower is 120.062515998m and the height of the hill is 57.8357059295m, we can say the height of the tower is the difference:

120.062515998 - 57.8357059295 = 62.2268100685 m