Question

ii) There is a flagpole on a 5 m hight tower. From one point on the ground, the
angle of elevation of the flag is 60° and from that point the elevation angle of
the tower is 45°. So find the height of the flagpole​

Answer 1

Answer:

5(√3-1)

Step-by-step explanation:

hope this helps

Answer 2

Recall that in Trigonometry:

$\sin \theta = \dfrac{\text{opposite}}{\text{hypothenuse}}$

$\cos \theta = \dfrac{\text{adjacent}}{\text{hypothenuse}}$

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

Given:

Height of the tower = 5m

angle of elevation of the tower= 45°

angle of elevation of the flag = 60°

Find the distance from the point on the ground to the tower:

Let the distance be D.

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

$\tan (45) = \dfrac{\text{5}}{\text{D}}$

$\text{D} = \dfrac{5}{\tan (45)}$

$\text{D} = 5 \text { m}$

Find the height of the tower and the flag:

Let the height be H.

$\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$

$tan(60) = \dfrac{H}{5}$

$\text{H} = 5\tan(60)$

$\text{H} = 5\sqrt{3} \text { m}$

Find the height of the flag:

$\text {Height }= 5\sqrt{3} - 5$

$\text {Height }= 5(\sqrt{3} - 1)$

$\text {Height }= 3.66 \text { m}$

Answer: The height of the flag pole is 3.66 m