Sample QuestionsSome Applications of Trigonometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
When the angle of elevation of the sun decreases from $60^{\circ}$ to $30^{\circ}$ the length of the shadow of the tower standing on the ground...........................
Answer: A.
View full solution →In the given figure $P$ and $Q$ represent............
- A
angle of elevation, line of vision
- B
angle of depression, horizontal line
- ✓
line of vision, angle of elevation
- D
horizontal line, angle of depression
Answer: C.
View full solution →In the given figure $\tan \theta=$..........
- ✓
$\frac{12}{5}$
- B
$\frac{5}{13}$
- C
$\frac{12}{3}$
- D
$\frac{5}{12}$
Answer: A.
View full solution →A ladder is placed along a wall such that its upper end is touching the wall at $4 m$ high. The length of the ladder is $5 m$. Then the foot of the ladder is ............... $m$ away from the ground.
Answer: A.
View full solution →There is a house, with height $x$ opposite to the hill. The height of the hill is $h$. The angle of elevation of the top of the hill from the bottom of the house is $\alpha$ and the angle of elevation of the top of the house from the bottom of the hill is $\beta$ then the value of $\frac{h}{x}$ is......................
- A
$1$
- ✓
more than $1$
- C
less than $1$
- D
Answer: B.
View full solution →A slope makes an angle of measure $30^{\circ}$ with the ground. On walking .....................$m$ on the slope, one can reach of a height $\frac{4}{a} m .\left(\frac{8}{9}, \frac{6}{9}, 8\right)$
View full solution →From the top of the tower $30 m$ height, the angle of depression of a ship is $60^{\circ}$. The distance of the ship from the tower is............................. m. $(5 \sqrt{2}, 5 \sqrt{3}, 10 \sqrt{3})$
View full solution →From a point on the ground $200 m$ away from the foot of a tower, the angle of elevation of the top of the tower is $30^{\circ}$. The height of the tower is................. m. $\quad\left(\frac{300}{\sqrt{2}}, \frac{100}{\sqrt{3}}, \frac{200}{\sqrt{3}}\right)$
View full solution →The ratio of the height of a tower and its shadow is $\sqrt{3}: 1$. Then the angle of the elevation of the sun is.......................... $\left(30^{\circ}, 90^{\circ}, 60^{\circ}\right)$
View full solution →In the given figure, the minimum distance to reach a point ' $C$ ' to a point ' $A$ ' is................ $\left(a, 2 a, \frac{a}{2}\right)$
View full solution →In a right angle triangle, the measure of the side opposite to angle $30^{\circ}$ is half of the hypotenuse.
View full solution →From the top of the tower, the angles of depression of two houses A and B on east and west sides of it are observed to be $30^{\circ}$ and $60^{\circ}$. Then the house $B$ is closer than the house A from the tower.
View full solution →When the length of the shadow of a tree is equal to the height of the tree, the angle of elevation of the sum is $60^{\circ}$.
View full solution →The angle of elevation of the sun is $\alpha$ at $8$ O'clock and $\beta$ at $10$ O'clock in the morning. Then $\alpha<\beta$.
View full solution →The angle of elevation of a house from a point A on the ground is $45^{\circ}$. The distance of a house from $A$ is $x$ and the height of a house is $y$. Then $x>y$.
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 $30^\circ$. Find the height of the tower.
View full solution →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 $30^\circ$.
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 is $60^\circ$. Find the height of the tower.
View full solution →An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. Find the height of the chimney?
The angle of elevation of the top of a building from the foot of the tower is $30^\circ $ and the angle of elevation of the top of the tower from the foot of the building is $60^\circ $. If the tower is $50\ m$ high, find the height of the building.
View full solution →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.
View full solution →From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20\ m$ high building are $45^\circ $ and $60^\circ $ respectively. Find the height of the tower
View full solution →A $1.5\ m$ tall boy is standing at some distance from a $30\ m$ tall building. The angle of elevation from his eyes to the top of the building increases from $30^\circ $ to $60^\circ $ as he walks towards the building. Find the distance he walked towards the building.
View full solution →A kite is flying at a height of $60\ m$ 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.
View full solution →
| $A$ |
$B$ |
| $Q.1. A$ horizontal ray is parallel to $......... .$ |
$(a)$ horizontal level |
| $Q.2. $ The line drawn from the eye of an observer to the point in the object viewed by observer is called $......... .$ |
$(b)$ observer |
| |
$(c)$ The line of sight |
| $A$ |
$B$ |
| $Q.1.$ When the point being viewed is below the horizontal level $........$ will be formed. |
$(a)$ Angle of deviation |
| $Q.2.$ When the point being viewed is above the horizontal level $.......$ will be formed. |
$(b)$ Angle of elevation |
| |
$(c)$ Angle of depression |
| $A$ |
$B$ |
| $Q.1.$ Aditya says that "The angle of elevation of top of the house from me is $60^{\circ}$ and that of the flying pigeon is $45^{\circ}$ ". Then $......... .$ |
$(a)$ The height of flying pigeon is more than the house. |
| $Q.2.$ From the terrace of a house, the angle of elevation of top of the tree is $30^{\circ}$ then $...$ |
$(b)$ The height of flying pigeon is less than the house. |
| |
$(c)$ The tree is more taller than house. |
| $A$ |
$B$ |
$Q.1.$ The angle of elevation of the top of a tower from a truck driver is $30^{\circ}$. After some times it is found to be $45^{\circ}$. Then the truck driver is walking
 |
$(a)$ The distance of car $A$ is more than car $B.$ |
$Q.2.$ From the top of the high rise building the angles of two cars $A$ and $B$ are $45^{\circ}$ and $60^{\circ}$. If cars $A$ and $B$ are on the same side of the building, then from the bottom of the building $.....$
 |
$(b)$Towards the tower. |
| |
$(c)$ The distance of car $B$ is more than car $A$. |
| $A$ |
$B$ |
| $Q.1.$ When the height of the house and the length of its shadow re equal, the angle of elevation of the sun is $......... .$ |
$(a)$ more than $45^\circ $ |
| $Q.2.$ After $3$ o'clock at afternoon the length of the shadow of the pillar is |
$(b) 45^\circ $ |
| |
$(c)$ increases |