Question

From the top of a bldg. 60ft high, two observers are seen on the ground. The angle of depression to the two observer are 54 degrees and 24 degrees. If the two observers and the bldg. are standing on horizontal ground and if the two observers are on the same side of the bldg. how far are the observers from each other?
I need your help how to illustrate and solve it.

Answer 1

Point A = top of the building.

Two observers are at point C and D. We have to find the distance CD which is 'x'. Angle of depressions are drawn at point A. Their alternate angles are at point C and D.

Now consider two right angled triangles i.e. $\Delta ABC$ and $\Delta ABD$.

**$\Delta ABC$**

tan (54°) = 60/y

$\Rightarrow$ y = 60/ tan (54°)

$\Rightarrow$ y = 43.6 ft ...(1)

**$\Delta ABD$**

tan (24°) = 60/(x+y)

$\Rightarrow$ (x+y) = 60/ tan (24°)

$\Rightarrow$ (x+y) = 134.76 ft.

Putting value of y from eq. (1), we get:

$\Rightarrow$ x = 134.76 – 43.6

$\Rightarrow$ x = 91.16 ft is the required answer.