Heights and Distances — Important Questions

sin θ, cos θ, tan θ

In height and distance problems, we primarily use sin θ (opposite/hypotenuse), cos θ (adjacent/hypotenuse), and tan θ (opposite/adjacent) as they directly relate to the sides we need to find.

12 m

Using tan(angle of elevation) = height/shadow length, we get tan45° = h/12. Since tan45° = 1, h = 12 m. The height equals the shadow length only because the angle is exactly 45°, ruling out the other options.

60√3 m

Using tan 30° = height/distance. tan 30° = 1/√3, so distance = 60/(1/√3) = 60√3 m ≈ 103.92 m

Angle of elevation is measured upward from horizontal, Angle of depression is measured downward from horizontal

Angles of elevation and depression are always measured from the horizontal line, with elevation going up and depression going down. In practical problems, these are typically acute angles (less than 90°).