Question

a flagstaff is placed at one corner of a rectangular playground 40 m long and 30 m wide. if the angle of elevation of the top of the flagstaff from the opposite corner is 30 degrees. find the height of the flagstaff.​

Answer 1

Ans

A flagstaff of placed at one corner of a rectangular playground 40m long and 30m wide. If the angle of elevation of the top of flag staff from the opposite corner of 30°, find height of the flagstaff.  

(The question is complete and I have cross checked the question. )

I made a slanted ground so that I can make the flagstaff's height be clear. But this way I only see one triangle being formedd in the figure. I also drew a diagonal for the rectangle. Since rectangle is slanted so I took the angle of elevation from the opposite corner from the diagonal ( not from the ground's length)

Answer 2

The height of flagstaff=11.96 m

Step-by-step explanation:

Let height of flagstaff=h

In triangle ACD

AB=h

BC=40 m

AC=AB+BC=h+40

CD=30 m

$\frac{AC}{CD}=tan30^{\circ}$

Using

$\frac{Perpendicular\;side}{Base}=tan\theta$

$\frac{h+40}{30}=\frac{1}{\sqrt 3}$

Using $tan30^{\circ}=\frac{1}{\sqrt 3}$

$h+40=30\sqrt 3$

$h=30\sqrt 3-40$

$h=11.96 m$

Hence, the height of flagstaff=11.96 m

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