Length of ladder

Draw triangle ABC. here, AB = Wall BC = Ground AC = Ladder and measure angle C = 30

therefore, sin C = AB/AC Sin 30 = 3/AC 1/2 = 3/AC (sin30 = 1/2) AC =3 x 2 so, AC = Ladder = 6 m

In a 30, 60, 90 triangle, the side opposite the 30 degree angle is 1/2 the hypotenuse. Ed Gray

Height at which the ladder touches the wall $=3m$
Angle of inclination $(\theta)=30^\circ$
$\sin \theta = \frac{Height}{Hypotenuse}$
$\Rightarrow \sin 30^\circ = \frac{3}{L}$ [Let L be the length of the ladder.]
$\Rightarrow \frac{1}{2} =\frac{3}{L}$
$\Rightarrow L = 3*2$
$\Rightarrow L= 6m$
So, Length of the Ladder is $\boxed {L=6m}$ .