Question

A man stands 9m away from a flag pole. He observes that angle of elevation of the top of the pole is 28degree and the angle of depression of the bottom of the pole is 13degree . Calculate the height of the pole.

Answer 1

height of the pole is 10.8 m

Answer 2

Answer:

6.862 m

Step-by-step explanation:

Refer the attached figure

A man stands 9m away from a flag pole. i.e. AC = BE = 9 m

He observes that angle of elevation of the top of the pole is 28degree and the angle of depression of the bottom of the pole is 13degree i.e. ∠DAE = 28° and ∠ACB = 13°

AB = CE

In ΔABC

$Tan \theta = \frac{AB}{AC}$

$Tan 13 = \frac{AB}{9}$

$0.23086= \frac{AB}{9}$

$0.23086 \times 9= AB$

$2.077= AB=EC$

In ΔBDE

$Tan \theta = \frac{DE}{BE}$

$Tan 28 = \frac{DE}{9}$

$0.5317= \frac{DE{9}$

$0.5317 \times 9= DE$

$4.785= DE$

Height of pole = DE+EC=4.785+2.077=6.862 m

Hence he height of the pole is 6.862 m