Question

A kite is flying at a height of 90 m from the ground level, attached to a string inclined at 60° angle to the horizontal. Find the length of the string.

Answer 1

Given:

Height of kite (vertical) = 90 m.

String makes angle 60° with horizontal.

Let the string length = OP (hypotenuse of right triangle).

Step-wise calculation:

1. In right triangle OMP.

`sin 60^circ = "Opposite side"/"Hypotenuse"`

= `"MP"/"OP"`

2. So, OP = MP

`sin 60^circ = 90/(sqrt(3)/2`

3. `OP = 90 × 2/sqrt(3)`

= `180/sqrt(3)`

= `60sqrt(3)`

4. Numerical value:

`sqrt(3) ≈ 1.732`

⇒ OP ≈ 60 × 1.732

= 103.92 m.

The length of the string = `60sqrt(3)` m ≈ 103.92 m.