R S Aggarwal and Veena Aggarwal Solutions for Exercise 1: Exercise 14

From the top of a building $\mathrm{AB}, 60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to be $30°$ and $60°$, respectively. If the horizontal distance between $\mathrm{AB}$ and $\mathrm{CD}$ is $x \mathrm{m}$, then find the value of $x$ correct to one decimal place. [Take $\sqrt{3}=1.732$]

From the top of a building $\mathrm{AB}, 60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to be $30°$ and $60°$, respectively. Find the height of the lamp post,

From the top of a building $\mathrm{AB}, 60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to be $30°$ and $60°$, respectively. Find the difference between the heights of the building and the lamp post.

A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from $30°$ to $45°$ in $12$ minutes and the time taken by the car to reach the tower is $k(\sqrt{3}+1) \min$, find the value of $k$.

An aeroplane is flying at a height of $300 \mathrm{m}$ above the ground. Flying at this height the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are $45°$ and $60°$ respectively. The width of the river is _____ $\mathrm{m}$ [Use $\sqrt{3}=1.732$]Enable GingerCannot connect to Ginger Check your internet connection
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From a point on the ground the angles of elevation of the bottom and top of a communication tower fixed on the top of a $20 \mathrm{m}$ high building are $45°$ and $60°$ respectively. Find the height of the tower. [Take $\sqrt{3}=1.732$]

From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be $45°$ and $30°$ respectively. Find the height of the hill in $\mathrm{km}$.

If at some time of the day the ratio of the height of a vertically standing pole to the length of its shadow on the ground is $\sqrt{3}:1$ then find the angle of elevation of the sun at that time.