Multiple choice

A man is standing on the top of a raised platform such that his eyes are 3 m high from the horizontal ground level and at a horizontal distance of 30 m from a tree. The angle of elevation of the top of the tree from his eyes is 30°. Estimate the height of the tree.

  1. 17.16 m

  2. 24.6 m

  3. 20.32 m

  4. 21.94 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The height of the tree above the eye level is 30 * tan(30) = 30 * (1/sqrt(3)) = 10 * sqrt(3) approx 17.32 m. Total height = 17.32 + 3 = 20.32 m.

AI explanation

The horizontal level difference forms a right triangle where the height of the tree above the man's eyes is found using tan(30°), meaning the vertical addition is 30 divided by √3, or 10√3. Since his eyes are already 3 m above the ground, the total height of the tree is 3 + 10√3. Using √3 as 1.732, the height becomes 3 + 17.32 = 20.32 m.

Keep practicing — related questions