Embibe Experts Solutions for Chapter: Applications of Trigonometry, Exercise 1: Exercise

Rehman observed the top of a temple at an angle of elevation of $30°$, when the observation point is $24\mathrm{m}$. away from the foot of the temple. Find the height of the temple.

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making $30°$ angle with the ground. The distance between the foot of the tree and the top of the tree on the ground is $6\mathrm{m}$. Find the height of the tree before falling down.

The distance between two points $\mathrm{A}$ and $\mathrm{B}$on the same side of a river bank is  $40 \mathrm{m}$. There is a point $\mathrm{C}$ on the opposite, parallel river bank such that $\angle \mathrm{BAC}=60°$ and $\angle \mathrm{ABC}=30°$.Find the width of the river.

An observer spots a balloon moving at a height of $90 \mathrm{m}$ above the horizon. If at a certain time the angle of elevation made by the balloon with the observer’s eyes is $45°$ which reduces to $30°$ after some time then find the distance covered by the balloon.

Two poles of equal heights are standing opposite to each other on either side of the road, which is $120$ feet wide. From a point between them on the road, the angles of elevation of the top of the poles are $60°$ and $30°$ respectively. Find the height of the poles and the distances of the point from the poles.

You are observing top of your school building at an angle of elevation $\alpha$ from a point which is at $d$ meter distance from the foot of the building. Which trigonometric ratio would you like to consider, to find the height of the building? 

A ladder of length $x$ meters is leaning against a wall making angle $\theta$ with the ground. Which trigonometric ratio would you like to consider to find the height of the point on the wall the ladder is touching?

If from the top of a tower $50$ m high, the angles of depression of two objects due north of the tower are respectively $60°$ and $45°$, then the approximate distance between the objects is _____.