The length of a string between a kite and a point on the roof of the building10 m high is 180 m. If the string makes an angle θ with the level ground suchthat tan θ = 4/3 how high is the kite from the ground?

Given:

Length of the string, l = PK = 180 m

To find: Height of the kite from ground

Solution:

In Δ KPR,

∠ KPR = θ,

KP = 180 m and tan θ = 4 / 3

tan θ = 4 / 3

= opposite / adjacent

Hypotenuse = √ (4 ² + 3 ² )

= 5

sin θ = opposite / hypotenuse

= 4 / 5

⇒ sin θ = KR / KP

KR / 180 = 4 / 5

∴ KR = (4 × 180) / 5

= 144 m

In rectangle PQLR,

PQ = RL = 10 m (Opposite sides of a rectangle)

∴ KL = KR + RL = (144 + 10) m

= 154 m

∴ The height of the kite from the ground is 154 m.