Class 10

Math

All topics

Some Applications of Trigonometry

The angle of elevation of a tower from a point $A$ due south of it, is $x$, from a point $B$ due east of $A$, is $y$. If $AB=l,$ then the height $h$ of the tower is given by

- $cot_{2}y−cot_{2}x l $
- $tan_{2}y−tan_{2}x l $
- $cot_{2}y−cot_{2}x 2l $
- None of these

In right angles $△OAP$

$∠OAP=x⇒hOA =cotx⇒OA=hcotx$ ...(1)

In right angled $△OBP$

$∠OBP=y⇒hOB =coty⇒OB=hcoty$ ...(2)

In right angles $△OAB$

$AB_{2}+OA_{2}=OB_{2}⇒l_{2}+h_{2}cot_{2}x=h_{2}cot_{2}y$

$⇒h_{2}(cot_{2}y−cot_{2}x )=l_{2}⇒h=cot_{2}y−cot_{2}x l $