2016 · Q65
Two observers are stationed due north of a tower (of height x metre) at a distance y metre from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal to
Elementary MathematicsTrigonometry
- A(√(2) - 1)/2
- B(√(3) - 1)/2
- C(√(3) + 1)/2
- D1
Explanation
If the nearer observer is d from the tower base, tan45° = x/d gives d = x. The farther observer gives tan30° = x/(d+y), so x = (x+y)/√3. Hence y = x(√3−1) and x/y = 1/(√3−1) = (√3+1)/2, option C.