Question

The length of a string between a kite and a point on the ground is 90m. If the string makes an angle Ø with the ground level such that tan Ø = 15/8, how high is the kite?

Answer 1

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Answer 2

Given:

Length of string = 90m

Tanθ  = 15/8

To Find:

Height of the Kite

Solution

Tan θ = 15/8 = BC/AB = h/AB

h = ABtanθ

In ΔABC

AC² = AB² + BC²

90² = AB² + h²

AB² = 90² - h ²

Substituting the value of h -  

h = √90² - h²tanθ

= h²( 1 + tan²θ) = 90²tan²θ

Again, substituting value of tan -  

h² = 8100 x 225/289

h = 90 x 15/17

= 1350/17

= 79.41

Answer: The kite is around 75m high