Example 1 · level 1
From a point 62 m away from the foot of a tower in Guwahati, the angle of elevation of the top is 45°. Find the height of the tower (in m).
Show solution
- tan 45° = h ÷ 62
- 1 = h ÷ 62 → h = 62 m.
Answer: 62 m
CLASS 10 MATHS · SOME APPLICATIONS OF TRIGONOMETRY
Heights and distances
Draw the right triangle. tan θ = height ÷ distance; sin θ = height ÷ slant length. Use tan 30° = 1/√3, tan 45° = 1, tan 60° = √3.
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Worked examples
Example 2 · level 2
From a point 31√3 m from the foot of a tree, the angle of elevation of its top is 30°. Find the height of the tree (in m).
Show solution
- tan 30° = h ÷ 31√3
- 1/√3 = h ÷ 31√3 → h = 31 m.
Answer: 31 m
Example 3 · level 3
A kite on a 72 m string makes an angle of 30° with the ground during Makar Sankranti. Assuming the string is straight, how high is the kite (in m)?
Show solution
- sin 30° = h ÷ 72
- h = 72 × 1/2 = 36 m.
Answer: 36 m