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.
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