Embibe Experts Solutions for Exercise 1: West Bengal Board-2018

If the ratio of the length of the shadow of a tower and height of the tower is $\sqrt{3}:1$, find the angle of elevation of the sun.

The length of the shadow of a post becomes $3 \mathrm{meters}$ smaller when the angle of elevation of the Sun increases from $45°$ to $60°$. Find the height of the post.

A man standing on a railway bridge $5\sqrt{3} \mathrm{meters}$ high, observes the engine of a train at an angle of depression $30°$. But after $2 \mathrm{seconds}$, he observes the engine at an angle of depression $45°$ on the other side of the bridge. Find the speed of the train.

From a quay of a river, $600$ metres wide, two boats start in two different directions to reach the opposite side of the river. The first boat moves to make an angle of $30°$ with this bank and the second boat moves to make an angle $90°$ with the direction of the first boat. What will be the distance between the two boats when both of them reach the other side?

The length of the flag post at the roof of a three-storied building is $3.6$ metre. The angles of elevation of the top and foot of the post are $50° \mathrm{and} 45°$ respectively from a point on the road. Find the height of the building. $[\mathrm{Take} \tan 50° = 1.2]$

If the angle of elevation of a cloud from a point $h$ metres above a lake is $\alpha$ and the angle of depression of its reflection in the lake is $\beta$. Prove that the distance of the cloud from the point of observation is $\frac{2h \sec \alpha }{\tan \beta -\tan \alpha }$.

The heights of two towers are $180$ metres and $60$ metres respectively. If the angle of elevation of the top of the first tower from the foot of the second tower is $60°$, then find the angle of elevation of the top of the second tower from the foot of the first.