2024 · Q46
A vertical pole of length 80 m is situated on the horizontal plane. The base of the pole is at P. There are two points A and B such that P, A, B are on the same straight line. Let the angles of elevation of top of the pole from A and B be α and β (α > β) respectively. If PA = 64 m and AB = 36 m, then what is (α + β) equal to?
Elementary MathematicsTrigonometry
- A60°
- B90°
- C120°
- D135°
Explanation
A is nearer the pole: tanα = 80/PA = 80/64 = 5/4. B is farther: PB = 64+36 = 100, so tanβ = 80/100 = 4/5. Since tanα × tanβ = (5/4)(4/5) = 1 with both angles acute, β = 90° − α. Thus α + β = 90° — option B.