The angle of depression of a car parked on the road from the top of a $150m$ high tower is $30^\circ$ . The distance of the car from the tower $($in metres$)$ is :
- A$50\sqrt{3}$
- ✓$150\sqrt{3}$
- C$150\sqrt{2}$
- D$75$
Answer: B.
View full solution →Question types
Some Application of Trigonomertry question types
262 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
262
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
211 Q→02Assertion (A) & Reason (B) MCQ
7 Q→03True False[1 Marks ]
4 Q→04Fill In The Blanks[1 Marks ]
2 Q→051 Marks Question
1 Q→063 Marks Question
12 Q→075 Marks Questions
8 Q→08Case study (4 Marks)
17 Q→Sample Questions
Some 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 $150m$ high tower is $30^\circ$ . The distance of the car from the tower $($in metres$)$ is :
- A$50\sqrt{3}$
- ✓$150\sqrt{3}$
- C$150\sqrt{2}$
- D$75$
Answer: B.
View full solution →A kite is flying at a height of $30m$ from the ground. The length of string from the kite to the ground is $60m.$ 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 →A tower stands vertically on the ground. From a point on the ground which is $25 m$ away from the foot of the tower, the angle of elevation of the top of the tower is found to be $45^\circ$ . Then the height $($in meters$)$ of the tower is :
- A$25\sqrt{2}$
- B$25\sqrt{3}$
- ✓$25$
- D$12.5$
Answer: C.
View full solution →A ladder makes an angle of $60^\circ$ with the ground when placed against a wall. If the foot of the ladder is $2 m$ away from the wall, then the length of the ladder $($in metres$)$ is :
- A$\frac{4}{\sqrt{3}}$
- B$4\sqrt{3}$
- C$2\sqrt{2}$
- ✓$4$
Answer: D.
View full solution →Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion : In the figure, if $BC = 20m,$ then height $AB$ is $11.56m.$
Reason : $\tan\theta=\frac{\text{AB}}{\text{BC}}=\frac{\text{perpendicular}}{\text{base}}$ where $\theta$ is the $\angle\text{ACB}$
Assertion : In the figure, if $BC = 20m,$ then height $AB$ is $11.56m.$
Reason : $\tan\theta=\frac{\text{AB}}{\text{BC}}=\frac{\text{perpendicular}}{\text{base}}$ where $\theta$ is the $\angle\text{ACB}$
- ✓Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: A.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$ .Mark the correct choice as:
Assertion: If the length of shadow of a vertical pole is equal to its height, then the angle of elevation of the sun is $45^{\circ}$
Reason: According to pythagoras theorem, $h ^2= I ^2+ b ^2$ where $h =$ hypotenuse, $I =$ length and $b =$ base
Assertion: If the length of shadow of a vertical pole is equal to its height, then the angle of elevation of the sun is $45^{\circ}$
Reason: According to pythagoras theorem, $h ^2= I ^2+ b ^2$ where $h =$ hypotenuse, $I =$ length and $b =$ base
- ABoth assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- ✓Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion $(A)$ is false but reason $(R)$ is true.
Answer: B.
View full solution →Statement A (Assertion) : A ladder $16 m$ long just reaches the top of a vertical wall. If the ladder makes an angle of $60^{\circ}$ with the wall, then the height of the wall is $8 m$.
Statement R (Reason): The value of $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$.
Statement R (Reason): The value of $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$.
- ABoth assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- ✓Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion (A) is false but reason $(R)$ is true.
Answer: B.
View full solution →Statement A (Assertion) : If a vertical tower of height $50 m$ casts a shadow of length $50 \sqrt{3} m$, then the angle of elevation of the Sun is $60^{\circ}$.
Statement R (Reason): If the angle of elevation of the Sun decreases, then the length of shadow of a tower increases.
Statement R (Reason): If the angle of elevation of the Sun decreases, then the length of shadow of a tower increases.
- ABoth assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- CAssertion $(A)$ is true but reason $(R)$ is false.
- ✓Assertion (A) is false but reason $(R)$ is true.
Answer: D.
View full solution →Statement A (Assertion): The height of an observer is $h m$. He stands on a horizontal ground at a distance $\sqrt{3} h m$ from a vertical pillar of height $4 h m$. The angle of elevation of the top of the pillar as seen by the observer is $60^{\circ}$.
Statement $R$ (Reason): The value of $\tan 60^{\circ}=\sqrt{3}$.
Statement $R$ (Reason): The value of $\tan 60^{\circ}=\sqrt{3}$.
- ✓Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- BBoth assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- CAssertion $(A)$ is true but reason $(R)$ is false.
- DAssertion (A) is false but reason $(R)$ is true.
Answer: A.
View full solution →Write ‘True’ or ‘False’ and justify your answer.
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
Write ‘True’ or ‘False’ and justify your answer.
The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.
The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.
Write ‘True’ or ‘False’ and justify your answer.
If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged.
If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged.
Write ‘True’ or ‘False’ and justify your answer.
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
In fig. the angles of depressions from the observing positions $O_1$ and $O_2$ respectively of the object $A$ are _________, _________.
View full solution →In fig. the angles of depressions from the observing positions $O _1$ and $O _2$ respectively of the object A are _________, _________.
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 $30^o.$
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° and 60° respectively. Find the height of the tower
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 $60^o$ Find the length of the string, assuming that there is no slack in the string.
View full solution →A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle $30^o$ with it. The distance between the foot of the tree to the point where the top touches the ground is $8 \ m$. Find the height of the tree.
View full solution →A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the further time taken by the car to reach the foot of the tower from this point.
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance traveled by the balloon during the interval.
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 →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° to 60° as he walks towards the building. Find the distance he walked towards the building.
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of 60° to the ground. What should be the length of the slides in each case?
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$ respectively. Find the height of the poles and the distances of the point from the poles.
View full solution →There exist a tower near the house of Shankar. The top of the tower AB is tied with steel wire and on the ground, it is tied with string support. One day Shankar tried to measure the longest of the wire AC using Pythagoras theorem.
(i) In the figure, the length of wire AC is: (take BC = 60 ft)
(ii) What is the area of ABC?
OR
What is the length of AP?
(iii) What is the area of a △POC?
(i) In the figure, the length of wire AC is: (take BC = 60 ft)
(ii) What is the area of ABC?
OR
What is the length of AP?
(iii) What is the area of a △POC?
Teewan, Arun and Pankaj were celebrating the festival of Diwali in open ground with firecrackers. There is a pedestal in the ground. All of sudden Teewan stands on a pedestal and releases a sky lantern from the top of the pedestal.
Based on the above information, answer the following questions.
(i) If the position of Pankaj is 25 m away from the base of the pedestal and Zr = 30°, then find the height of the pedestal.
(ii)If the vertical height of sky lantern from the top of pedestal is 12 m and∠y = 30°, then distance between Teewan and sky lantern ?
(iii) If ∠q = 60° and position of Arun is 15 m away from the base of pedestal, then find the height of pedestal.
OR
Which one is a pair of angles of depression?
There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing
on the top of 50 m high temple, observed from the top that angle of depression of the top and foot of other temple are 30° and 60° respectively. (Take √3 = 1.73)
Based on the above information, answer the following questions.
(i) Measure of angle ADF is equal to
(ii) Measure of angle ACB is equal to
(iii) Width of the river is
OR
Height of the other temple is
Ronit is the captain of his school football team. He has decided to use a 4-4-2-1 formation in the next match. The igure below shows the positions of the players in a 4-4-2-1 formation on a
coordinate grid.One square box represents 1 square unit.
(i)What is the distance between the two centre forward positions in Ronit’s plan?
(ii)What is the area (in square units) of the football field enclosed by the lines joining the two centre back positions and the goalkeeper’s position?
OR
A ball hit from the left full back position travels uninterrupted to the right centre forward
position. What can be the minimum distance traveled by the all?
(iii)Which two positions are on the line x+5y-5=0= 0?
coordinate grid.One square box represents 1 square unit.
(i)What is the distance between the two centre forward positions in Ronit’s plan?
(ii)What is the area (in square units) of the football field enclosed by the lines joining the two centre back positions and the goalkeeper’s position?
OR
A ball hit from the left full back position travels uninterrupted to the right centre forward
position. What can be the minimum distance traveled by the all?
(iii)Which two positions are on the line x+5y-5=0= 0?
Rahul is driving a car. On his way, he approaches a tall building and observes that Rajesh is
standing at the top of that building. A signboard beside the building read - Angle of depression =60°. The distance from the building at which Rahul stops his car is 50cm.
(i) Is the angle of elevation from Rahul's car to the top of building, where Rajesh is standing the same as the angle of depression ?
(ii) What is the length of the line of sight ?
OR
What is the height of the tower ?
(iii) Will the angle of elevation increase or decrease as the car approaches the building ?
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