Exercise

The angle of elevation of a ladder leaning against a wall is $60°$ and the foot of the ladder is $10 \mathrm{m}$ away from the wall. If the length of the ladder is $a \mathrm{m}$, then find the value of $a$?

An aeroplane flying at the height of $3000 \mathrm{m}$ above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are $60°$ and $45°$ respectively. Then the height of the lower plane from the ground is

If $\sin \theta =\frac{1}{2}$, then write the value of $(3 {\cot }^2\theta +3).$

If the height of the tower and the distance of the point of the observation from its foot, both are increased by $20\%$, then the angle of elevation does not change.

$\left(\frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta }\right)\left(\frac{1-\sin \theta }{\cos \theta }\right)=$?

If $\lambda \cos \theta =1$ and $\lambda \sin \theta =\sqrt{3}$, find the positive value of $\lambda$.

A tower is $50\sqrt{3} \mathrm{metres}$ high. If the angle of elevation of its top from the point $50 \mathrm{m}$ away from its foot is $k°$, then find the value of $k$.

If the length of shadow of a pole on a level ground is equal to the length of the pole, the angle of elevation of sun is: