AB is a straight road leading to the foot of a tower at C. A being at the distance of 200m from C and B is 125m nearer from C .The angle of elevation of the top of yheu tower at B is double than at A . find the height of the tower.
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Answer:
The height of the tower is 100 m.
Step-by-step explanation:
tan A = h / 200
tan B = h / 75
We know that ∠B = 2 ∠A
tan 2 A = ( 2 tan A ) / ( 1 - tan² A )
200 tan A = 75 tan 2 A
200 tan A = 75 * ( 2 tan A ) / ( 1 - tan² A ) / : tan A
( we will divide both sides of the equation by tan A )
200 = 150 / ( 1 - tan² A )
1 - tan² A = 0.75
tan² A = 0.25
tan A = 0.5
h = 200 tan A = 200 * 0.5 = 100 m
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