Question

Application of Trigonometry

Height and Distance

Solve this problem

Find height

Answer 1

Trigonometry:


Tan ∅= Perpendicular/Base

Cot∅= Base/Perpendicular


Tan60° = √3

Cot 60° = 1/√3

Tan 45° = 1

Answer 2

Answer:

h = 25√3m

Step-by-step explanation:

Let DC = h metres and BC = x metres.

Given, ∠DBC = 60°, ∠DAC = 30°, AB = 50 m.

(i)

From ΔDBC,

tan 60° = h/x

√3 = h/x

h = x√3  

(ii)

From ΔDAC,

tan 30° = (h/50 + x)

1/√3 = h/50 + x

√3h = 50 + x

h = (50 + x)/√3  

On solving (i) &(ii), we get

x√3 = (50 + x)/√3

3x = 50 + x

2x = 50

x = 25

Substitute x = 25 in (i), we get

h = x√3

h = 25√3

Therefore, h = 25√3m.

Hope it helps!