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 30⁰ =

∴ Q = H √3 …………. (i)

Step 2: Next, in Δ ABC, tan ∠ ABC =

∴ tan 45⁰ =

∴ 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) = a² – b² )

∴ H =

∴ H =

∴ H =

∴ H = 9.56 m

Therefore, height of the tower is 9.56 m

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