Embibe Experts Solutions for Chapter: Some Applications of Trigonometry, Exercise 1: Nagaland Board-2018

When a pole $6 \mathrm{m}$ high casts a shadow $2\sqrt{3} \mathrm{m}$ long on the ground, then the angle of elevation of the sun is 

In the adjoining figure, find the value of $x$.

The horizontal distance between two poles is$15 \mathrm{m}$ . The angle of depression of the top of the first pole as seen from the top of the second pole is $30°$. If the height of the second pole is $24 \mathrm{m}$, find the height of the first pole. [Use $\sqrt{3}=1.73$ ]

From two points $P$ and $Q$ at distances of $a$ and $b$ respectively from the base of a tower and in the same straight line with it, the angles of elevation of the top of the tower are complementary. Prove that the height of the tower is $\sqrt{ab}$.

An aeroplane flying horizontally at a height of $2500 \mathrm{m}$ above the ground is observed at an elevation of $60°$. After $15 \mathrm{seconds}$, the elevation is observed to be $30°$. Find the speed of the aeroplane in $\mathrm{km}/\mathrm{hr}$. [Use $\sqrt{3}=1.73$]

A ladder leans against a wall making an angle of $45°$ with the ground. It reaches $\left(\sqrt{3}-\sqrt{2}\right) \mathrm{m}$ higher when the angle with the ground is $60°$. How long is the ladder?

From the top of a $7 \mathrm{m}$ high building, the angle of depression of the foot of a cable tower $\left(7\sqrt{3}+7\right) \mathrm{m}$ high is $45°$. Find the angle of elevation of the cable tower from the top of the building.

From a point on the ground, the angles of elevation of the top and the bottom of a flagstaff fixed at the top of a $20 \mathrm{m}$ high pillar are $60°$ and $\theta$ respectively. If the height of the flagstaff is $\left(\sqrt{3}-1\right)$ times the height of the pillar, find the value of $\theta$.