Question

A building and a tree are on opposite sides of a road of width 10m. The tree subtends an angle of 30° at the top of the building and the angle of elevation of the top of the top of the building from the bottom of the tree is 60°. What is the height of the tree?

a) 2 root3 m
b) 10 root3/3 m
c) 20 root3/3 m
d) 20 root3 m​

Answer 1

Answer:

c) (20√3) / 3 m

Step-by-step explanation:

Given:

AB = CE = Tree = x

CD = Building = x + y

BC = AE = Road = 10 m

Angle DAE = 30°

Angle DBC = 60°

In triangle BCD,

tan 60° = x+y / 10

10√3 = x+y ...... equ 1

In triangle ADE,

tan 30° = y/10

10/√3 = y.......equ 2

substitute equ 2 in equ 1

x + 10/√3 = 10√3

√3x + 10 /√3 = 10√3

√3x + 10 = 10√3×√3

= 10 × 3

√3x + 10 = 30

√3x = 30 - 10 = 20

x = 20 / √3 = (20√3) / 3 m

Hope it helps you:)