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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