**Q) A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower. **

**Ans:**

Let’s start from the diagram for the question:

Let ‘s take CD as the tower of height H and AD be the flagstaff of 7 m.

Point B is Q distance away from C.

**Step 1:** Let’s start from In Δ BCD, tan ∠ DBC =

∴ tan 30^{0} =

∴ Q = H √3 …………. (i)

**Step 2:** Next, in Δ ABC, tan ∠ ABC =

∴ tan 45^{0} =

∴ 1 =

∴ Q = H + 7 …………. (ii)

*( Note: Here we calculate Q in terms of H. When we will get all H terms together and value of H will be calculated.) *

**Step 3:** From equation (i) and equation (ii), we get:

H √3 = H + 7

∴ H √3 – H = 7

∴ H (√3 – 1) = 7

∴ H =

∴ H =

∴ H =

∴ H = (by (a + b) ( a – b) = a^{2} – b^{2} )

∴ H =

∴ H =

∴ H =

**∴ H = 9.56 m**

**Therefore, height of the tower is 9.56 m**

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