The angles of elevation of the top of a tower from two points on the same straight path are 30° and 60°. If the points are 800 m apart, find the height of the tower
Correct: B
Let h be the height. From the first point: h/x = tan30° ⇒ x = h√3. From the second point: h/(x - 800) = tan60° ⇒ x - 800 = h/√3. Substitute x = h√3 into the second equation: h√3 - 800 = h/√3 ⇒ Multiply by √3: 3h - 800√3 = h ⇒ 2h = 800√3 ⇒ h = 400√3 m.