angle of elevation of the top of the hill at the foot of tower is 60 degrees and the angle of elevation of tower from the foot of the hill is 30 degrees. if tower is 50m high find the height of hill
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Let AB is the Tower of height = h = 50 m.
And, let the Height of Hill CD = H m.
Distance between The root of the tower and hill = BC
Now,
In ΔABC
∠C = 30°
TAN(C) = AB/BC
⇒ TAN(30) = 50/BC
⇒ 1/√3 = 50 /BC
⇒ BC = 50√3 m.
Now,
In ΔBCD,
∠B = 60°
Tan(B) = CD/BC
⇒ Tan(60) = H/BC
⇒ BC√3 = H
⇒ H = 50√3*√3 = 150 m.
And, let the Height of Hill CD = H m.
Distance between The root of the tower and hill = BC
Now,
In ΔABC
∠C = 30°
TAN(C) = AB/BC
⇒ TAN(30) = 50/BC
⇒ 1/√3 = 50 /BC
⇒ BC = 50√3 m.
Now,
In ΔBCD,
∠B = 60°
Tan(B) = CD/BC
⇒ Tan(60) = H/BC
⇒ BC√3 = H
⇒ H = 50√3*√3 = 150 m.
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