CDS 2026 (I) Elementary Mathematics, question 44

Topic: Heights and distances

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Q44

At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be $\frac{5}{6}$ . On walking $70$ m towards the tower, the tangent of the angle of elevation of the top of the tower is found to be $\frac{9}{8}$ . What is the height of the tower ?

(a) 225 mCorrect answer
(b) 270 m
(c) 300 m
(d) 330 m

Solution.

Answer: (a) 225 m

Let the tower height be h.
The initial horizontal distance is $6h/5$ and the final distance is $8h/9$ .
Their difference is 70 m.
Thus $6h/5 - 8h/9 = 70$ , or $14h/45 = 70$ , giving $h = 225m$ .