Class 10

Math

All topics

Some Applications of Trigonometry

The angle of depression of two post $P$ and $Q$ at a distance of $2$ meter on the same side of a road from a balloon $(B)$ vertically over the road are observed to be $45_{∘}$ and $60_{∘}$. What is the height of the balloon?

- $3−3 $
- $3 −1$
- $3+3 $
- $3 +1$

let the height of the balloon be $h$ and the point on ground be S

In $△PBS$

$tan45=PSBS $

$BS=PS=h$

In $△QBS$

$tan60=QSBS $

$BS=QS3 $

$QS=3 h $

Now, $PS−QS=2$

$h−3 h =2$

$h=3 −123 $

$h=3−123 (3 +1) $ (Rationalising)

$h=3+3 $