2019 · Q54
Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30°, and the angle of elevation to the top of the tower at C is 45°. What is the ratio of the height of the towers at B and C?
Elementary MathematicsTrigonometry
- A1:√3
- B1:3
- C1:2
- D1:2√3
Explanation
In a regular hexagon of side s, adjacent vertices are s apart (AB = s) while AC spans two edges, AC = s√3. Tower at B: h_B = AB·tan 30° = s/√3. Tower at C: h_C = AC·tan 45° = s√3. Ratio h_B : h_C = 1 : 3.