**Q) From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of ****20m high building are 45 ^{0} and 60^{0} respectively. Find the height of the transmission tower.**

**A****ns:**

**Step 1: **Let’s start by drawing a diagram for this question:

Here, we can see AB is 20 m high building and PA is the tower on top of building. Angle from Point C to point A is 45^{0} and to Point P is 60^{0}. We need to find height H of tower PA.

**Step 2:**

Let’s start from Δ ABC, here tan C =

∴ tan 45 =

∴ 1 =

∴ D = 20 m

**Step 3:**

Next, Let’s take in Δ PBC, here tan C =

∴ tan 60 =

∴

∴ 20√3 = 20 + H

∴ H = 20√3 – 20 = 20(√3 – 1) = 20 x 0.732 = 14.64m

**Therefore, the height of the transmission tower is 20(√3 – 1)m or 14.64m***Note: calculate value in decimal terms, only if it is given that √3 = 1.732 in the question.*

**Please do press “Heart” button if you liked the solution.**