Angle of Elevation

Q.

Two pillars of equal heights stand on either side of a road which is 100 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are ${60}^{\circ }$ and ${30}^{\circ }$. Find the height of each pillar and position of the point on the road.

1. The height of each pillar is 43.3 m and the point of observation is 28 m away from the first pillar.

2. The height of each pillar is 40.3 m and the point of observation is 25 m away from the first pillar.

3. The height of each pillar is 43.3 m and the point of observation is 25 m away from the first pillar.

4. The height of each pillar is 93.3 m and the point of observation is 25 m away from the first pillar.

Q.

An aeroplane at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the width of the river.

1. 524.34 m

2. 924.34 m

3. 324.34 m

4. 394.34 m

Q.

A person standing on the bank of the river observes that the angle of elevation of the top of a tree standing on the opposite bank is $60$ degrees. When he was 40m away from the bank he found the angle of elevation to be $30$ degrees. Find the width of the river.

1. $20$ m

2. $10$ m

3. $5$ m

4. $1$ m

Q. (a) What is dispersion of white light? What is the cause of dispersion? Draw a diagram to show the dispersion of white light by a glass prism.
(b) A glass prism is able to produce a spectrum when white light passes through it but a glass slab does not produce any spectrum. Explain why it is so.