Heights and Distances

Q. Question 14
A 15m high tower casts a shadow 24m long at a certain time and at the same time, a telephone pole casts a shadow 16m long. Find the height of the telephone pole.

Q.

A statue 2 m tall, stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of the statue is ${60}^{\circ }$ and from the same point the angle of elevation of the top of the pedestal is ${45}^{\circ }$. Find the height of the pedestal.

1. 2 / (√3 +1) m

2. 4 / (√3−1) m

3. 4 / (√3 + 1) m

4. 2 / (√3−1) m

Q.

The shadow of a tower is found to be $60m$ shorter when the Suns altitude changes from $30°$ to $60°$.

The height of the tower from the ground is approximately

1. $62m$

2. $301m$

3. $101m$

4. $75m$

5. $52m$

Q.

Question 8
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is ${60}^{\circ }$ and from the same point the angle of elevation of the top of the pedestal is ${45}^{\circ }$. Find the height of the pedestal.

Q. Question 18
The lower window of a house is at a height of 2m above the ground and its upper window is 4m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be ${60}^{\circ }$ and ${30}^{\circ }$, respectively. Find the height of the balloon above the ground.

Q.

From a point P on the ground, the angle of elevation of the top of a 20 m tall building is ${30}^{\circ }$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff is ${45}^{\circ }$. Find the height of the flag. (You may take $\sqrt{3}$ = 1.732)

1. 20√3 m

2. 20 m

3. 14.64 m

4. 10 m

Q. From a certain spot, the top of a flagpole has an angle of elevation of 30°. After moving 10 m in a straight line towards the flagpole, the top has an angle of elevation of 50° . Find the height of the flagpole.
(Use sin 50° = 0.766, cos 50° = 0.643, tan 50° = 1.192)

1. Height = 9.39m and distance = 11.19m
2. 11.19 m
3. 29.82 m
4. 15.63 m

Q.

A technician has to repair a light on a pole of height 10 m. She needs to reach a point 2 m below the top of the pole to undertake the repair work. The length of the ramp that she should use which, when inclined at an angle of ${30}^{\circ }$ to the horizontal, would enable her to reach the required position, is______ m.
(You may take $\sqrt{3}$ = 1.73)

1. 8 m
2. 16 m
3. 12 m
4. 10 m

Q.

A statue, $1.6\mathrm{m}$ tall, stands on the top of the pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60°$ and from the same point, the angle of elevation of the top of the pedestal is $45°$. Find the height of the pedestal.

1. height of the pedestal $=0.2(\sqrt{7}–1)\mathrm{m}$

2. height of the pedestal $=0.8(\sqrt{3}+1)\mathrm{m}$

3. height of the pedestal $=1.6(\sqrt{5}+1)\mathrm{m}$

4. height of the pedestal $=1.9(\sqrt{11}-1)\mathrm{m}$

Q.

Two observers one at P and the other at Q were 500m apart when they observed the flash of an enemy gun at R. If ∠RPQ = 45^o and ∠RQP = 30^o, find out how far P was from the enemy gun.

1. 256.34

2. 258.76

3. 243.56

4. 198.78

Q. Question 14
An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

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 m

2. 50 m

3. 35 m

4. 45 m

Q. Question 8
If $\Delta ABC$ is right angled at C, then the value of cos(A+B) is

(A) 0
(B) 1
(C) $\frac{1}{2}$
(D) $\frac{\sqrt{3}}{2}$

Q.
Find the value of x.

1. $\frac{{45}^o}{x}=tan{45}^o$
2. $x=\frac{tan{40}^o}{{45}^o}$
3. $x={45}^o\times tan{40}^o$
4. $x=\frac{{45}^o}{tan{40}^o}$

Q. A girl walked from the point B to C and then she moved 20 m to reach the point D. She is looking at the top of the building. Which of the following will be her line of sight?

1. BC
2. CD
3. AD
4. AC

Q. A hill slopes upwards at an angle of ${30}^{\circ }$ with ground. If he walks 100 m and reaches the top of the hill, calculate the height of the hill.

1. 30 m
2. 40 m
3. 50 m
4. 60 m

Q.

When the sun is at an elevation of ${40}^{\circ },$ the shadow of a flag post in 15 m. The length of the shadow when sun is at an elevation of ${45}^{\circ }$ will be $[Tan{40}^{\circ }=0.84,Tan{45}^{\circ }=1]$

1. 13.6 cm

2. 12.6 cm

3. 11.6 cm

4. 14.6 cm

Q.

The angles of elevation of the top of a tower at two points, which are at distances $a$ and $b$ from the foot in the same horizontal line and on the same side of the tower, are complementary. The height of the tower is

1. $ab$

2. $\sqrt{ab}$

3. $\sqrt{\frac{a}{b}}$

4. $\sqrt{\frac{b}{a}}$

Q.

In $\Delta ABC,AB=10cm,\angle A={40}^{\circ },\angle B={110}^{\circ }.$ The area of the triangle will be equal to ______. $[Tan{40}^{\circ }=0.84,Tan{70}^{\circ }=2.75]$

1. $60.47c{m}^2$

2. $68.19c{m}^2$

3. $70.8c{m}^2$

4. $50.15c{m}^2$

Q. A boy is looking at the top of a building which is 10 m high.
From the figure, the distance between the boy and the building will be_______ .

1. 5 m
2. 10 m
3. 15 m
4. 20 m

Q.

In $\Delta ABC,AB=10cm,\angle A={40}^{\circ },\angle B={80}^{\circ }.$ Find the area of triangle ABC.

$\left[\begin{array}{c}tan{40}^{\circ }=0.83\\ tan{80}^{\circ }=5.6\end{array}\right]$

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

Q. As observed from the top of a $75$ m high lighthouse from the sea-level, the angles of depression of two ships are ${30}^{\circ }$ and ${45}^{\circ }$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Q. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is ${30}^{\circ }$ [1 MARK]

Q. A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of ${68}^{\circ }$ with the ground. Find the height, upto which the ladder reaches. [2 MARKS]

Q. Find $PQ$, if $AB=150m,\angle P={30}^{\circ }$ and $\angle Q={45}^{\circ }$

1. $978.8$
2. $524.4$
3. $409.8$
4. $279.9$

Q. If $\cos 3\theta =\frac{\sqrt{3}}{2}$, $0°<3\theta <90°$, the value of $\theta$ (in degrees) is

1. 10

Q.

In $\Delta ABC,AB=15cm,\angle A={30}^{\circ },\angle B={130}^{\circ }.$ The area of the triangle will be equal to $\left[\begin{array}{c}Tan{30}^{\circ }=0.57\\ Tan{50}^{\circ }=1.2\end{array}\right]$

1. $152.18c{m}^2$

2. $122.13c{m}^2$

3. $132.8c{m}^2$

4. $142.12c{m}^2$

Q.

When the sun is at an elevation of ${50}^{\circ },$ the shadow of a flag post is 20 m.The height of the flag post is, $[Tan{50}^{\circ }=1.2]$

1. 20 m

2. 24 m

3. 12 m

4. 10 m

Q.

In an isosceles triangle$ABC$, the angle $A$at the vertex is$70°$. Find the base angles $\angle Band\angle C$ taking $AB=AC$