Question

27. A tower and a building on the opposite side of road are situated. The angles of
depression from the top of tower at the roof and base of building are 45° and 60°
respectively. If height of building is 12 m then find the height of the tower. (13=
1.732)​

Answer 1

Let AB is a building of height 12 m. CE is a tower.

Let ED = h m.

The angles of depression from point E of top of tower at the roof and base on building are 45° and 60° respectively.

Now

∠XEA = ∠EAD = 45° (Alternate angle)

∠XEB = ∠EBC = 60° (Alternate angle)

Let BC = x and ED = h m

AB = CD = 12 m

From right angled ΔEAD,

tan 45°= ED/AD

l = h/x

⇒ h = x …(i)

From right angled ΔEBC,

tan 60° = (h + 12)/BC

√3 = (h + 12)/x

(h + 12)/h (Put the value of x from equation (i))

⇒ √3h = h + 12

⇒ √3h – h = 12

⇒ h[1.732 – 1] = 12

⇒ h = 12/0.732

= 16.393 m

Hence, height of tower

= EC = CD + ED

= 12 + 16.393

= 28.393 m

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