Question

a vertical pedestal stands on the ground and is surmounted by a vertical flag staff of height 5 m.At a point on the ground the angles of elevation of the bottom and top of the flag staff are 30 degree and 60 degree respectively.Find the height of the pedestal.

Answer 1

Answer:

2.5 ft

Step-by-step explanation:

The figure for the given scenario is shown below.

There are two right angled triangles, ΔACD and ΔBCD

The height of flag staff is represented by segment AB, BC is the height of pedestal stand , D is a point on the ground that makes angles 30° and 60° with the bottom and top of staff at B and A respectively.

AB = 5 ft. Let the height of pedestal stand be $x$ ft and the distance of point D from the bottom of stand be $y$ ft as shown in the figure.

Now, from ΔACD,

$tan(60)=\frac{AC}{CD}\\ \sqrt{3}=\frac{5+x}{y}\\ \sqrt{3}y=5+x$

From ΔBCD,

$tan(30)=\frac{BC}{CD}\\\frac{1}{\sqrt{3}}=\frac{x}{y}\\y=\sqrt{3}x$

Plug in the value of $y$ in the first equation and solve for $x$.

$\sqrt{3}y=5+x\\\sqrt{3}(\sqrt{3}x)=5+x\\3x=5+x\\2x=5\\x=\frac{5}{2}=2.5 \textrm{ ft}$.

Therefore, the height of the pedestal stand is 2.5 ft.