the angle of elevation ''a'' of a vertical tower from a point on the ground is such that its tan - Maths - Some Applications of Trigonometry

Question

the angle of elevation ''a'' of a vertical tower from a point on
the ground is such that its tan is 5/12 on walking 192 metres
towards the tower in the same straight line , the tangent of the
angle of elevation "b" is found to be 3/4 find the height of the
tower

Lalit Mehra · Accepted Answer

Dear Student!

Let the height of the tower be h m and BC = x m Suppose A and B be the position of the points on the ground subtending angles of elevation of the tower such that $\tan A = \frac{5}{12}$ and $\tan B = \frac{3}{4}$ respectively Given, AB = 192 m In Î” BCD, $\tan B = \frac{CD}{BC} (∵ \tan θ = \frac{Perpendicular}{Base}) ∴ \frac{3}{4} = \frac{h}{x} \Rightarrow x = \frac{4 h}{3} (1)$ In Î” ACD, $\tan A = \frac{CD}{AC} ∴ \frac{5}{12} = \frac{h}{192 + x} \Rightarrow 12 h = 5 (192 + x) \Rightarrow 12 h = 960 + 5 x \Rightarrow 12 h = 960 + 5 (\frac{4 h}{3}) (Using (1)) \Rightarrow 12 h - \frac{20 h}{3} = 960 \Rightarrow \frac{36 h - 20 h}{3} = 960 \Rightarrow \frac{16 h}{3} = 960 \Rightarrow h = \frac{960 \times 3}{16} = 180$ Thus, the height of the tower is 180 m Cheers!

the angle of elevation ''a'' of a vertical tower from a point on the ground is such that its tan is 5/12. on walking 192 metres towards the tower in the same straight line , the tangent of the angle of elevation "b" is found to be 3/4 . find the height of the tower