Calculating Heights and Distances

Q.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are ${30}^{\circ }$ and ${45}^{\circ }$, respectively. If the bridge is at a height of 6 m from the banks, find the width of the river.

1. $6m$

2. $6\sqrt{3}m$

3. $3\sqrt{3}m$

4. $(6+6\sqrt{3})m$

Q.

There are 2 ships on either side of a lighthouse. If the angles of elevation of the lighthouse from both the ships are ${30}^{\circ }$ and ${45}^{\circ }$ respectively. If the height of lighthouse is 'h' and distance between the two ships is 'd', the ratio of 'd' to 'h' up to 1 decimal place is ___

Q.

The tops of two poles of height 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:

1. 6m

2. 8m

3. 12m

4. 10m

Q.

A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is ${60}^{\circ }$. Find the length of the string, assuming that there is no slack in the string.

1. $20\sqrt{3}$ m

2. $30\sqrt{3}$ m

3. $60$ m

4. $30$ m

Q.

From the top of a lighthouse 'H' m tall, a person observes the angle of depression of a boat to be ${60}^{\circ }$. Another person who is $\frac{H}{3}$ m from the top of a lighthouse observes the angle of depression of another boat directly behind the first boat to be ${45}^{\circ }$. Find the distance between the two boats.

(Take $\sqrt{3}$ = 1.7)

1. H/10

2. H/2

3. 1.7H

4. 0.6H

Q.

The angle of elevation of the top of a tree from a point A on the ground is ${60}^{\circ }$ .On walking 20 m away from its base, to a point B, the angle of elevation changes to ${30}^{\circ }$. Find the height of the tree.

1. 10

2. 20

3. 30

4. 40

Q.

The shadow of a tower standing on a level ground is found to be 60 m longer when the Sun’s altitude is ${30}^{\circ }$ than when it is ${60}^{\circ }$. Find the height of the tower.

1. 30√3 m

2. 20 m

3. 30 m

4. 20 m

Q.

An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is ${45}^{\circ }$. What is the height of the chimney?

1. 40

2. 35

3. 45

4. 50

Q.

Two poles are erected from the ground. The length of the longer pole is 10m. If the distance between the tips of the poles is 6m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is ${30}^{\circ }$, find the length of the second pole.

Q. From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

1. $7m$
2. $\sqrt{3}m$
3. $(7+7\sqrt{3})m$
4. $(7-7\sqrt{3})m$