Two pillars of equal height stand on either side of a roadway which is 150 m wide. At a point in the road between pillars, the elevations of the pillars are x∘ and y∘ so that tan x∘=2/5,tan y∘=3/5, then the height of each pillar is:

Correct option is D

Distance between the pillars =150 m

tan x =2/5,

tan y=3/5,

Concept and Formula Used:

Height and distance concept;

Trigonometry ratio,

tan⁡ θ = $$\frac {\text {Perpendicular}}{\text{Base}}$$​​

Solution:

ATQ,

​$$\tan{\left(x^\circ\right)} = \frac{2}{5} = \frac{\text{Perpendicular}}{\text{Base}} \\\ \\\tan{\left(y^\circ\right)} = \frac{3}{5} = \frac{\text{Perpendicular}}{\text{Base}}$$​​

Now,

2p = 3q …. (given)

p/q = 3a/2a

And 5p + 5q = 150

15a + 10a = 150

a = 6

so, p = 18m

q = 12m

height of each pillar = 36 m