2017 · Q100
From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive kilometre-stones on the opposite sides of the aeroplane are observed to be a and p. The height of the aeroplane above the road is
Elementary MathematicsTrigonometry
- A(tanα + tanβ)/(tanα tanβ)
- B(tanα tanβ)/(tanα + tanβ)
- C(cotα cotβ)/(cotα + cotβ)
- D(cotα + cotβ)/(cotα cotβ)
Explanation
If the plane is at height h, the two kilometre-stones are h·cotα and h·cotβ away horizontally on opposite sides. Hence h(cotα + cotβ) = 1 km, so h = 1/(cotα + cotβ) = tanα·tanβ/(tanα + tanβ): option B. Option A inverts the fraction.