From a point on level ground, the tangent of the angle of elevation of the top of a tower is 5/6. On walking 70 m towards the tower, the tangent of the angle of elevation of the top of the same tower is 9/8. What is the height of the tower?
A.225 m✓ Correct
B.270 m
C.300 m
D.330 m
Explanation
Let height = h and distance from second point to base = x. Then tan(α) = h/x = 9/8 so x = 8h/9. From first point, distance = x + 70, and tan(β) = h/(x+70) = 5/6, so x + 70 = 6h/5. Thus 6h/5 - 8h/9 = 70. LCM 45: (54h - 40h)/45 = 70, 14h/45 = 70, h = 70·45/14 = 225 m.
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