Question

★QUESTION★

A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower.


$SOLVE \: with \: full \: answr$
​

Answer 1

$\bf\huge{Question:-}$

A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower.

$\bf\huge{answer:-}$

∆BAP

$\implies$tan 30°=$\frac{BA}{AP} = \frac{h}{l} = \frac{1}{√3}$

$\implies\sqrt{3}h$

∆DAP

Tan 45°=$\frac{DA}{AP} = \frac{7m+h}{√3h} = 1$

$\implies$ $\sqrt{3h}=7+h$

$\implies\frac{7(√3+1)}{(√3+1)(√3-1)}$

$\implies$ h=3.5(√3+1)m

Answer 2

Step-by-step explanation:

AB be the flagstaff of height 7 m on the tower and Dbe the point on the plane making an angle of elevation of the top of the flagstaff is 45° and angle of elevation of the bottom of the flagstaff is 30°. Let CD = x, AB = 7 and ∠BDC = 30° and ∠ADC = 45°. So we use trigonometric ratios.