2026 · Q44
A person walking along a straight road observes that at two consecutive kilometer-stones the angles of elevation of a hill in front of him are 30° and 60° respectively. What is the height of the hill?
Elementary MathematicsTrigonometry
- A3√3 km
- B2√3 km
- C√3 km
- D√3/2 km
Explanation
Let the hill's height be h and the distance of the nearer milestone from the hill's base be d − 1 km. Then h/(d − 1) = tan 60° = √3 and h/d = tan 30° = 1/√3, so d = h√3. Substituting, h√3 − 1 = h/√3, i.e. h(√3 − 1/√3) = 1, giving h = √3/2 km, option D.