Subject Experts Solutions for Chapter: Height and Distance, Exercise 1: Target Exercise

What will be the angle of elevation of sun at the instant, when the length of the shadow of a building is $\frac{1}{\sqrt{3}}$ times its height?

An eagle flying $100 \mathrm{m}$ above the ground, makes an angle of depression $\theta$ at a point on the ground. If the shortest distance between the eagle and the point on the ground is $200 \mathrm{m}$, then the value of $\theta$ is

A building which is $30 \mathrm{m}$ high was observed from a point on the ground. Observer found the angle of elevation of a point on the second floor of the building which is $10 \mathrm{m}$ above the ground same as the angle subtended by the rest of the building above the point $P$. If the height of the observer is to be ignored, approximate distance between the observer and the foot of the building is $\left(\mathrm{Take} \sqrt{3}=1.732\right)$

A cat saw a rat when it was exactly at the middle of the vertical tower. At that moment the angle of elevation as observed by the cat was $30°$. The cat ran a certain distance towards the tower to chase the rat, which is at the top of the tower. If the cat which is now $20 \mathrm{m}$ away from the foot of the tower finds the angle of elevation of the rat to be $60°$, what distance cat ran?

Two poles at points $A$ and $B$ stands on a horizontal place. $C$ and $D$ are two points between them. The angle of elevation of the top of the poles as observed from the point $C$are $30°, 60°$ and from point $D$ are $60°$ and $45°$. If $CD=30 \mathrm{m}$, then $AB$ is equal to

A man who is $6 \mathrm{ft}$ tall found the angle of elevation of the top of a tower to be $45°$. If the angle of depression at the foot of the tower as observed by the man is $30°$, what is the height of the tower?

A man standing on the lighthouse observes the angle of elevation of a boat coming towards the lighthouse to be $60°$ from $30°$ in $15 \min$. How much time will the boat take to reach the foot of the lighthouse?

A $50 \mathrm{m}$ high pole which is above a $250 \mathrm{m}$ high building observed by an observer standing at a height of $300 \mathrm{m}$. If the top of the building and the top of the pole subtends equal angle i.e., $\theta$ at the observer, then the horizontal distance of the observer from the pole is