Question

The length of a string attached to a kite and a point on the ground is 58 m. If the string makes an angle A with the ground such that tan A = `20/21` at what height is the kite?

Answer 1

Given:

Length of the string (hypotenuse) = 58 m

tan⁡A = `20/21` where A is the angle between the string and the ground.

We are to find the height of the kite, i.e., the vertical side (opposite to angle A)

Step 1: Use the identity

tan A = `"opposite"/"adjacent" = 20/21`

Opposite = 20k

Adjacent = 21k

Hypotenuse = use Pythagoras     ...[Let k be a number.]

Hypotenuse = `sqrt((20k)^2 + (21k)^2)`

Hypotenuse = `sqrt(400k^2 + 441k^2)`

Hypotenuse = `sqrt(841k^2)`

Hypotenuse = 29k

29 = 58 = k

k = `58/29` = 2

Height = 20k

= 20 × 2

= 40 m