Angle of Elevation

Q. The angle of elevation of a jet plane from a point A on the ground is ${60}^{\circ }$. After a flight of 30 seconds, the angle of elevation changes to ${30}^{\circ }$. If the jet plane is flying at a constant height of $3600\sqrt{3}metres$, find the speed of the jet plane. [4 MARKS]

Q. When the sun's altitude changes from ${30}^{\circ }$ to ${60}^{\circ }$, the length of the shadow of a tower decreases by $70m$. What is the height of the tower?

1. $140m$
2. $60.6m$
3. $20.2m$
4. $35m$

Q.

From a boat, 300 meter away from a vertical cliff, the angles of deviation of the top and the foot of a vertical pillar at the edge of the cliff are 55 and 54 respectively. Find the height of the pillar.

1. 219.6 m

2. 209.8 m

3. 119.9 m

4. 189.4 m

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.

The height of the cliff is
I. The angle of elevation of the cliff from a fixed point F is ${45}^{\circ }$
II. After going up towards a distance of 1000 m at an inclination of ${30}^{\circ }$, the angle of elevation is ${60}^{\circ }$

1. Only statement I is required

2. Only statement II is required

3. Both statements I and II are required

4. Neither of the statement is sufficient

Q.

A ladder 20 m long is placed against a vertical wall of height 10 metres. Find the distance between the foot of the ladder and the wall and also the inclination of the ladder with the ground.

1. 10 m,

2. 10 m,

3. 5 m,

4. None of these

Q.

$sin{60}^{\circ }cos{45}^{\circ }tan{45}^{\circ }cot{60}^{\circ }sec{30}^{\circ }cosec{90}^{\circ }$

1. $\frac{1}{\sqrt{6}}$

2. $\frac{\sqrt{3}}{\sqrt{2}}$

3. $\frac{\sqrt{2}}{\sqrt{3}}$

4. $\sqrt{6}$

Q. ABDE is a trapezium.​​​​​​ with $AE\parallel BD$ and $ED\perp BD$, and AC is drawn parallel to the side DE.

Find the values of $\text{cot}\theta and\text{cosec}\theta$ respectively, from the above figure.

1. $\frac{5}{4},\frac{5}{4}$
2. 2, $\frac{5}{2}$
3. $\frac{4}{3},\frac{5}{3}$
4. $\frac{5}{2}$, 2

Q.

A point B on the level ground is x m away from the foot of a h meter tall tower. If the angle of elevation of the top of the tower from the point B is B°, then the height of the tower is ______ m.

1. x tanB

2. x/tanB

3. tanB/x

4. none of these

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. [Take $\sqrt{3}$=1.732] [3 MARKS]

Q.

A ladder of length $16$ units is resting against a wall of height $8$ units. The angle made by the leg of the ladder with the ground is

1. ${60}^{\circ }$

2. ${30}^{\circ }$

3. ${45}^{\circ }$

4. ${90}^{\circ }$

Q. If the angle of elevation of a cloud from a point 200 m above a lake is ${30}^{\circ }$ and the angle of depression of its reflection in the lake is ${60}^{\circ }$, then the height of the cloud above the lake is ___.

Q.

The height of the building is 100$\sqrt{3}$ft, What is the angle of elevation from a point on the level ground 100ft away from the base of the building?

1. ${60}^{\circ }$

2. ${30}^{\circ }$

3. ${50}^{\circ }$

4. ${70}^{\circ }$

Q.

From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the angle of depression to the foot of the tower. The height of the tower is ___.

1. 25m

2. 75m

3. 50m

4. 100m

Q.

An observer 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. Write the answer correct to the nearest whole number. [3 MARKS]

Q. In the figure, $PQ$ and $RS$ are two mirrors placed parallel to each other. An incident ray $AB$ strikes the mirror $PQ$ at $B$, the reflected ray moves along the path $BC$ and strikes the mirror $RS$ at $C$ and again reflects back along $CD$. Prove that $AB\parallel CD$.

Q.

The figure gives the lengths of a tree and its shadow (in feet). Using the information given in the figure, find the value of $\theta$. (Hint : Use Tan $\theta$)

1. ${30}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. ${90}^{\circ }$

Q.

The angle of elevation of a tower of height m from the eye of two observers A and B on the same side of the tower are $\alpha$ and $\beta$. respectively. If the distance between the foot of the tower and the person nearer to tower is x and the distance between the tower and second person is y. Then,
The distance between the two people is :

1. $b(cot\alpha +cot\beta )$

2. $b(cot\beta -cot\alpha )$

3. $bcot\alpha$

4. $cot\beta$

Q.

A point B on the level ground is x m away from the foot of a h meter tall tower. If the angle of elevation of the top of the tower from the point B is B°, then the height of the tower is ______ m.

1. x tanB

2. x/tanB

3. tanB/x

4. none of these

Q.

ABDE is a trapezium with $AE\parallel BD$ and $ED\perp BD$, and AC is drawn parallel to the side DE.

Find the values of $\text{cot}\theta and\text{cosec}\theta$ respectively, from the figure.

1. 2, $\frac{5}{2}$

2. $\frac{4}{3},\frac{5}{3}$

3. $\frac{5}{4},\frac{5}{4}$

4. $\frac{5}{2}$, 2

Q.

The height of the cliff can be found out if the following information is given
I. The angle of elevation of the cliff from a fixed point F is ${45}^{\circ }$
II. After going up towards a distance of 1000 m at an inclination of ${30}^{\circ }$, the angle of elevation is ${60}^{\circ }$

1. Both statements I and II are required

2. Neither of the statement is sufficient

3. Only statement II is required

4. Only statement I is required

Q. ABDE is a trapezium​​​​​​ with $AE\parallel BD$ and $ED\perp BD$. Also, AC is drawn parallel to the side DE.

Find the values of $\text{cot}\theta and\text{cosec}\theta$, respectively, from the figure above.

Q.

A round ballon of radius r subtends an $\alpha$ at the eye of the observer while the an elevation of its centre $\beta$. The height of centre of the balloon is

1. $rsin\beta cosec\frac{\alpha }{2}$

2. $rsin\beta /2cos\alpha /2$

3. $rsin\beta /2cos\alpha$

4. $rsin\beta cos\alpha$

Q. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

1. 273m
2. 173m
3. 300m
4. 200m

Q. Length of the shadow of 15 m tall building is 15 m at 1 pm. What is the angle of elevation of the sun's rays with the ground at the time?

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${120}^{\circ }$
4. ${360}^{\circ }$

Q. An observer $\sqrt{3}m$ tall is $3m$ away from the pole $2\sqrt{3}m$ high. The angle of elevation of the top from the pole is:

1. ${45}^o$
2. ${30}^o$
3. ${15}^o$
4. ${60}^o$

Q.

The height of the building is 200\sqrt{3}ft, What is the angle of elevation from a point on the level ground 100ft away from the base of the building?

1. ${30}^{\circ }$

2. ${50}^{\circ }$

3. ${60}^{\circ }$

4. ${70}^{\circ }$

Q.

In the given figure h = ___ m.

1. $30\sqrt{3}$

2. $15\sqrt{3}$

3. $15$

4. $30$

Q.

Two poles of different heights are erected from the ground. If the smaller pole is 20 m high and distance between 2 poles are 10 m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is ${60}^{\circ }$, find the length of the second pole.

1. $20+\frac{10}{\sqrt{3}}m$

2. $20+5\sqrt{3}m$

3. $10+10\sqrt{3}m$

4. $20+10\sqrt{3}m$

Q.

A round ballon of radius r subtends an $\alpha$ at the eye of the observer while the an elevation of its centre $\beta$. The height of centre of the balloon is

1. $rsin\beta cosec\alpha /2$

2. $rsin\beta /2cos\alpha$

3. $rsin\beta cos\alpha$

4. $rsin\beta /2cos\alpha /2$