H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Heights & Distances, Exercise 1: EXERCISE

A man on the deck of a ship is $16 \mathrm{m}$ above water level. He observes that the angle of elevation of the top of a cliff is $45°$ and the angle of depression of the base is $30°$. Calculate the distance of the cliff from the ship and the height of the cliff. 

A person observed the angle of elevation of the top of a tower to be $30°$. He walked $50 \mathrm{m}$ towards the foot of the tower along level ground and found the angle of elevation of the top of the tower to be $60°$, Find the height of the tower.

A path separates two walls. A ladder leaning against one wall rests at a point on the path. It reaches a height of $90 \mathrm{m}$ on the wall and makes an angle of $60°$ with the ground. If while resting at the same point on the path, it were made to lean against the other wall, it would have made an angle of $45°$ with the ground. The height, it would have reached on the second wall is _____ $\mathrm{m}$ (Round off the final answer upto two decimal places)

A carpenter makes stools for electrician with a square top of side $0.5 \mathrm{m}$ and at a height $1.5 \mathrm{m}$ above the ground. Also each leg is inclined at an angle of $60°$ to the ground. Find the length of each leg and also the lengths of two steps to be put at equal distances in metres.

At the foot of a mountain the elevation of its summit is $45°$ after ascending $1000 \mathrm{m}$ towards the mountain up a slope of $30°$ inclination, the elevation is found to be $60°$. Find the height of the mountain.

There is a small island in the middle of a $100 \mathrm{m}$ wide river and a tall tree stands on the island. $\mathrm{P}$ and $\mathrm{Q}$ are points directly opposite each other on the two banks, and in line with the tree. If the angles of elevation of the top of the tree from $\mathrm{P}$ and $\mathrm{Q}$ are respectively $30°$ and $45°,$ find the height of the tree. 

From a building $60$ meters high, the angles of depression of the top and bottom of a lamp post are $30°$ and $60°$ respectively. Find the distance between the lamp post and the building. Also, find the difference of height between the building and the lamp post. 

A contractor plans to install two slides for the children to play in a park. For the children below the age of $5$ years, she prefers to have a slide whose top is at a height of $1.5 \mathrm{m},$ and is inclined at an angle of $30°$ to the ground, whereas for elder children, she wants to have a steep slide at a height of $3 \mathrm{m}$, and inclined at an angle of $60°$ to the ground. What should be the length of the slide in each case.