Question

The string of a kite is 80 m long. It makes 45° angle from the horizontal. Find the height of the kite from the ground.

Answer 1

Given:

String (hypotenuse) = 80 m

Angle with horizontal = 45°

Step-wise calculation:

1. Let the vertical height = h opposite side to the 45° angle. 

For a right triangle, h = string × sin 45°.

2. sin 45° = `sqrt(2)/2`.

3. h = `80 xx sqrt(2)/2` 

= `80/2 xx sqrt(2)`

= `40sqrt(2)` m

4. Numerical value:

`40sqrt(2) ≈ 40 xx 1.41421356`

= 56.5685 m

= 56.57 m

Height of the kite from the ground = `40sqrt(2)` m ≈ 56.57 m.