2021 · Q50
A vertical tower standing at the corner of a rectangular field subtends angles of 60° and 45° at the two nearer corners. If θ is the angle that the tower subtends at the farthest corner, then what is cot θ equal to?
Elementary MathematicsTrigonometry
- A1/2
- B2
- C2/√3
- D4/√3
Explanation
Let the tower height be h. Then h/AB = tan 60° gives AB = h/√3, and h/AD = tan 45° gives AD = h. The diagonal to the farthest corner is AC = √(h²/3 + h²) = 2h/√3. So cotθ = AC/h = 2/√3. Hence option C.