Question

A ladder is placed against a vertical tower. If the ladder makes an angle of 30 with the ground and reaches up to a height of 20 m of the tower, find the length of the ladder.

Answer 1

★ GIVEN

• A ladder is placed against a vertical tower

• Ladder makes an angle = PQR = 30degree

• Height of the tower = PR = 20m

★ TO FIND

• The length of the ladder

★ SOLUTION

We know that,

$\sf{ { \frac{Perpendicular}{Hypotenuse}= sin }}$

_____________

Where,

Perpendicular = PR

Hypotenuse = PQ

sin = 30degree

_____________

$\sf\rightsquigarrow{ \: sin \: 30\degree=\frac{PR}{PQ}}$

$\sf\rightsquigarrow{ \: \frac{1}{2} = \frac{20}{PQ}}$

$\sf\rightsquigarrow{ \: PQ = 20 \times 2}$

$\sf\rightsquigarrow{\:PQ = 40m}$

$\sf\therefore \:Length \: of \: the \: ladder \: is \: 40m.$