Sample QuestionsSome Application of Trigonomertry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The angle of depression of a car parked on the road from the top of a $150 m$ high tower is $30^{\circ}$. The distance of the car from the tower $($in metres$)$ is
- A
$50 \sqrt{3}$
- ✓
$50 \sqrt{3}$
- C
$150 \sqrt{2}$
- D
$75$
Answer: B.
View full solution →A ladder makes an angle of $60^{\circ}$ with the ground when placed against a w all. If the foot of the ladder is $2\ m$ away from the wall, then the length of the ladder $($in meters$)$ is:
- A
$\frac{4}{\sqrt{3}}$
- B
$4 \sqrt{3}$
- C
$2 \sqrt{2}$
- ✓
$4$
Answer: D.
View full solution →The angle of depression of a car, standing on the ground, from the top of a $75 m$ high tower, is $30^{\circ}$. The distance of the car from the base of the tower $($in $m .)$ is:
- A
$25 \sqrt{3}$
- B
$50 \sqrt{3}$
- ✓
$75 \sqrt{3}$
- D
Answer: C.
View full solution →A kite is flying at a height of $30\ m$ from the ground. The length of string from the kite to the ground is $60
\ m$ . Assuming that there is no slack in the string, the angle of elevation of the kite at the ground is
- A
$45^{\circ}$
- ✓
$30^{\circ}$
- C
$60^{\circ}$
- D
$90^{\circ}$
Answer: B.
View full solution →The angle of elevation of the top of a tower from a point on the ground, which is $30\ m$ away from the foot of the tower is $45^{\circ}$. The height of the tower $($in metres$)$ is
- A
$15$
- ✓
$30$
- C
$30 \sqrt{3}$
- D
$10 \sqrt{3}$
Answer: B.
View full solution →The ratio of the height of a tower and the length of its shadow on the ground is $\sqrt{3}: 1$. What is the angle of elevation of the Sun?
View full solution →If a tower $30 m$ high, easts a shadow $10 \sqrt{3} m$ long on the ground, then what is the angle of elevation of the sun?
View full solution →A ladder leaning against a wall, makes an angle of $60^{\circ}$ with the horizontal. If the foot of the ladder is $2.5 m$ away from the wall, find the length of the ladder.
View full solution →In Fig. $1, \text{AB}$ is a 6 m high pole and $\text{CD}$ is a ladder inclined at an angle of $60^{\circ}$ to the horizontal and reaches up to a point $D$ of pole. If $\text{AD}=2.54 m$, find the length of the ladder. $($Use $\sqrt{3}=1.732 )$
View full solution →In figure, a tower $A B$ is $20 m$ high and $B C$, its shadow on the ground, is $20 \sqrt{3} m$ long. Find the Sun's altitude.
View full solution →Find the length of the shadow on the ground of a pole of height 18 m when angle of elevation $\theta$ of the sun is such that $\tan \theta=\frac{6}{7}$.
View full solution →A moving boat is observed from the top of a $150\ m$ high cliff moving away from the cliff. The angle of depression of the boat changes from $60^{\circ}$ to $45^{\circ}$ in $2$ minutes. Find the speed of the boat in $m / h$.
View full solution →On a straight line passing through the foot of a tower, two points $C$ and $D$ are at distances of $4 m$ and $16 m$ from the foot respectively. If the angles of elevation from $C$ and $D$ of the top of the tower are complementary, then find the height of the tower.
View full solution →The angles of depression of the top and bottom of a $50 m$ high building from the top of a tower are $45^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower and thehorizontal distance between the tower and the building.
View full solution →A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as $60^{\circ}$ and the angle of depression of the base of hill as $30^{\circ}$. Find the distance of the hill from the ship and the height of the hill.
View full solution →The angle of elevation of an aero plane from a point $A$ on the ground is $60^{\circ}$. After a flight of $15$ seconds, the angle of elevation changes to $30^{\circ}$. If the aero plane is flying at a constant height of $1500 \sqrt{3} m$, find the speed of the plane in $km / hr$.
View full solution →From the top of a $7 m$ high building, the angle of elevation of the top of a cable tower is $60^{\circ}$ and the angle of depression of its foot is $45^{\circ}$. Determine the height of the tower.
View full solution →The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is $30^{\circ}$ than when it was $60^{\circ}$. Find the height of the tower.
View full solution →The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is $30^{\circ}$ and the angle of depression of its shadow in water of lake is $60^{\circ}$. Find the height of the cloud from the surface of water.
View full solution →An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are $45^{\circ}$ and $60^{\circ}$ respectively. Find the width of the river. [Use $\sqrt{3}=1.732$ ]
View full solution →The angle of elevation of the top $Q$ of a vertical tower $P Q$ from a point $X$ on the ground is $60^{\circ}$. From a point $Y, 40 m$ vertically above $X$, the angle of elevation of the top $Q$ of the tower is $45^{\circ}$. Find the height of the tower $P Q$ and the distance $P X$.
View full solution →Kite Festival
Kite festival is celebrated in many countries at different times of the year. In India, every year $14^{\text {th }}$ January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, three kites flying together.
In Fig. $5,$ the angles of elevation of two kites $($Points $A$ and $B)$ from the hands of a man $($Point $C)$ are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Taking $AD =50 m$ and $BE =60 m,$ find
$(1)$ the lengths of strings used $($take them straight$)$ for kites $A$ and $B$ as shown in the figure.
$(2)$ the distance $'d\ '$ between these two kites View full solution →Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point $O$.
Distance between the base of the tower and point O is 36 cm . From point O , the angle of elevation of the top of the Section B is $30^{\circ}$ and the angle of elevation of the top of Section $A$ is $45^{\circ}$.
Based on the above information, answer the following questions:
(i) Find the length of the wire from the point O to the top of Section B.
(ii) Find the distance $A B$.
OR
Find the area of $\triangle OPB$.
(iii) Find the height of the Section A from the base of the tower. View full solution →