At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be 5/6. On walking 70 m towards the tower, the tangent of the angle of elevation of the top of the tower is found to be 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 nearer point to the tower = d. Then h/d = 9/8, so d = 8h/9. From the farther point: h/(d + 70) = 5/6, so 6h = 5(d + 70) = 5d + 350. Substituting d = 8h/9: 6h = 5(8h/9) + 350 = 40h/9 + 350. Multiplying by 9: 54h = 40h + 3150, so 14h = 3150, giving h = 225 m.
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