You want to erect a pole of height $10\mathrm{m}$ with the support of three ropes. Each rope has to make an angle $30°$ with the pole. If the length of the rope is $k m$, then find the value of $k$.

Write youe answer up to two decimal places.

Suppose you are shooting an arrow from the top of a building at an height of $6\mathrm{m}$ to a target on the ground at an angle of depression of $60°.$ If the distance between you and the object is $k m$, then find the value of $k.$

Write your answer up to three decimal places.

A boat has to cross the river. It crosses the river by making an angle of $60°$ with the bank of river due to the stream of the river and travels a distance of $600$ m to reach the another side of the river. If the width of the river is $k m$, then find the value of $k$.

Write your answer up to three decimal places.

In the below figure, $\mathrm{AC}=6 \mathrm{cm}$, $\mathrm{AB}=5$ $\mathrm{cm}$ and $\angle \mathrm{BAC}=$ $30°.$ If the area of the triangle is $k {\mathrm{cm}}^2$, then find the value of $k$.

A $1.5\mathrm{m}$ tall boy is looking at the top of a temple which is$30$ meter in height from a point at certain distance. The angle of elevation from his eye to the top of the crown of the temple increases from $30°$ to $60°$as he walks towards the temple. If the distance he walked towards the temple is $k m$, then find the value of $k$.

Write your answer upto three decimal places.

A statue stands on the top of a $2\mathrm{m}$ tall pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60°$ and from the same point, the angle of elevation of the top of the pedestal is $45°.$ If the height of the statue is $k m$ then find the value of $k$.

Write your answer up to three decimal places.