Question

a vertical tower stands on a horizontal plane and is surmounted by a veritical flagstaff of height 5m from a point on the plane the angle of evlevation of the bottom and top of the flagstaff are respectively 30deg and 60deg . find the height of the power

Answer 1

See the attached file for solution. Thanks

Answer 2

The height is 2.5 m

Given:

Height of flagstaff = 5 m

Step-by-step explanation:

Let the height of the tower be h meters.

The following is the figure for the given problem.

We know that,

$\tan \theta=\frac{\text {Adjacent side}}{\text {Opposite side}}$

From triangle ABC,

$\tan 30=\frac{h}{B C}$

$h=B C\left(\frac{1}{\sqrt{3}}\right)$

$B C=\sqrt{3}(h)$

From triangle PBC,  

$\tan 60=\frac{P B}{B C}$

$\sqrt{3}=\frac{\mathrm{h}+5}{\mathrm{BC}}$

$B C \sqrt{3}=\mathrm{h}+5$

On substituting the value of BC, we get,

$\sqrt{3} h(\sqrt{3})+5$

$3 h=h+5$

$2 h=5$

$h=\frac{5}{2}$

$\therefore h=2.5 \ \mathrm{m}$