An observer measures angles of elevation of two tower of equal height from a point between the towers. If the angles of elevation are 60° and 30° and distance of nearer tower is 100 m then the height of each tower and the distance between the towers, respectively are

Let us draw a figure below as per given question.
Let AB = CD = h meter be the heights of the towers. E is a point such that DE = 100 meter;
∠CED = 60° and ∠AEB = 30°
Now, BE = x meter (say)
From right triangle CDE.
h = 100 tan 60°
⇒ h = 100√3 meter
From right triangle ABE,
x = h cot 30° put the value of h, we will get
x = 100√3 X √3
x = 100 X 3 = 300 meters
Distance between the tower = DE + EB = 100 + 300 = 400 meters
Height of the tower = h = 100√3 meter