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

A man in a boat rowing away from a light house $100 \mathrm{m}$ high takes $2$ minutes to change the angle of elevation of the top of the light house from $60°$ to $30°$. Find the speed of the boat in meters per minute. [Use $\sqrt{3}=1.732$]

A ladder that is $6 \mathrm{m}$ long is leaning against the side of a building making an angle of $60°$ with the ground. Determine how far the ladder's base is from the building, and how far up it is on the building.

From the top of a tower situated at a distance of $60$ metre from a house, the angle of elevation of the top of the house is $60°$ and the angle of depression of the bottom is $30°$. Find the heights of the tower and house. ($\sqrt{3}=1.732$)

If the angle of elevation of the sun changes from $45°$ to $60°$ the length of the shadow of a tower is decreased by $40$ metre. Find the height of the tower. ($\sqrt{3}=1.732$)

From one side of a river, the angle of elevation of the top of the tower on the opposite side is $45°$. On going back $30$ metre from the bank along the same straight line with the tower the angle of elevation becomes $30°$. Find the breadth of the river.

When the angle of elevation of sun is decreased from $60°$ to $30°$ the length of shadow of a rod is increased by $40$ metre. What is the height of the rod?

As observed from the top of a $100 \mathrm{m}$ high light house from the sea level, the angles of depression of two ships are $30°$ and $45°$. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. $[\text{Use} \sqrt{3}=1.732]$

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height $6 \mathrm{m}$. At a point on the plane, the angle of elevation of the bottom and top of the flag staff are $30°$ and $45°$ respectively. Find the height of the tower. Take $\sqrt{3}=1.73$