CBSE Class 10 Some Applications of Trigonometry Sure Shot Questions Set 02

Case Based MCQs

Case I : Read the following passage and answer the questions.
isit to Temple
There are two temples on each bank of a river. One temple is 50 50 m high. A man, who is standing on the top of 50 50 m high temple, observed from the top that angle of depression of the top and foot of other temple are 30 ∘ 30 ∘ and 60 ∘ 60 ∘ respectively. (Take 3 = 1.73 3 ​ =1.73 )

Question. Measure of \( \angle ADF \) is equal to
(a) \( 45^\circ \)
(b) \( 60^\circ \)
(c) \( 30^\circ \)
(d) \( 90^\circ \)
Answer: (c)

Question. Measure of \( \angle ACB \) is equal to
(a) \( 45^\circ \)
(b) \( 60^\circ \)
(c) \( 30^\circ \)
(d) \( 90^\circ \)
Answer: (b)

Question. Width of the river is
(a) \( 28.90 \) m
(b) \( 26.75 \) m
(c) \( 25 \) m
(d) \( 27 \) m
Answer: (a)

Question. Height of the other temple is
(a) \( 32.5 \) m
(b) \( 35 \) m
(c) \( 33.33 \) m
(d) \( 40 \) m
Answer: (c)

Question. Angle of depression is always
(a) reflex angle
(b) straight
(c) an obtuse angle
(d) an acute angle
Answer: (d)

Case II : Read the following passage and answer the questions.
Application of Trigonometry for Moving Car Rohit is standing at the top of the building observes a car at an angle of 30 ∘ 30 ∘ , which is approaching the foot of the building with a uniform speed. 6 6 seconds later, angle of depression of car formed to be 60 ∘ 60 ∘ , whose distance at that instant from the building is 25 25 m.

Question. Height of the building is
(a) \( 25\sqrt{2} \) m
(b) \( 50 \) m
(c) \( 25\sqrt{3} \) m
(d) \( 25 \) m
Answer: (c)

Question. Distance between two positions of the car is
(a) \( 40 \) m
(b) \( 50 \) m
(c) \( 60 \) m
(d) \( 75 \) m
Answer: (b)

Question. Total time taken by the car to reach the foot of the building from starting point is
(a) \( 4 \) secs
(b) \( 3 \) secs
(c) \( 6 \) secs
(d) \( 9 \) secs
Answer: (d)

Question. The distance of the observer from the car when it makes an angle of \( 60^\circ \) is
(a) \( 25 \) m
(b) \( 45 \) m
(c) \( 50 \) m
(d) \( 75 \) m
Answer: (c)

Question. The angle of elevation increases
(a) when point of observation moves towards the object
(b) when point of observation moves away from the object
(c) when object moves away from the observer
(d) None of these
Answer: (a)

Case III : Read the following passage and answer the questions.
Flying Pigeon
A boy 4 4 m tall spots a pigeon sitting on the top of a pole of height 54 54 m from the ground. The angle of elevation of the pigeon from the eyes of boy at any instant is 60 ∘ 60 ∘ . The pigeon flies away horizontally in such a way that it remained at a constant height from the ground. After 8 8 seconds, the angle of elevation of the pigeon from the same point is 45 ∘ 45 ∘ . (Take 3 = 1.73 3 ​ =1.73 )

Question. Find the distance of first position of the pigeon from the eyes of the boy.
(a) \( 54 \) m
(b) \( 100 \) m
(c) \( \frac{100}{\sqrt{3}} \) m
(d) \( 100\sqrt{3} \)
Answer: (c)

Question. If the distance between the position of pigeon increases, then the angle of elevation
(a) increases
(b) decreases
(c) remains unchanged
(d) can’t say
Answer: (b)

Question. Find the distance between the boy and the pole.
(a) \( 50 \) m
(b) \( \frac{50}{\sqrt{3}} \) m
(c) \( 50\sqrt{3} \) m
(d) \( 60\sqrt{3} \) m
Answer: (b)

Question. How much distance the pigeon covers in \( 8 \) seconds?
(a) \( 12.13 \) m
(b) \( 19.60 \) m
(c) \( 21.09 \) m
(d) \( 26.32 \) m
Answer: (c)

Question. Find the speed of the pigeon.
(a) \( 2.63 \) m/sec
(b) \( 3.88 \) m/sec
(c) \( 6.7 \) m/sec
(d) \( 9.3 \) m/sec
Answer: (a)

Assertion & Reasoning Based MCQs

Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given.
Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : If the height and length of the shadow of a man are the same, then the angle of elevation of the Sun is \( 45^\circ \).
Reason : The value of \( \tan 45^\circ = 0 \).
(a) a
(b) b
(c) c
(d) d
Answer: (c)

Question. Assertion : Mohini looks at a top of tree and angle made is \( 45^\circ \). She moves \( 10 \) m back and again looks at the top of tree, but this time angle made is \( 30^\circ \), then height of the tree is \( \frac{10}{\sqrt{3} - 1} \) m.
Reason : The angle of elevation and depression can be acute or obtuse angle.
(a) a
(b) b
(c) c
(d) d
Answer: (c)

Question. 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 \( 4h \) m. The angle of elevation of the top of the pillar as seen by the observer is \( 60^\circ \).
Reason : The value of \( \tan 60^\circ = \sqrt{3} \).
(a) a
(b) b
(c) c
(d) d
Answer: (a)

Question. 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 \( 60^\circ \).
Reason : If the angle of elevation of the Sun decreases, then the length of shadow of a tower increases.
(a) a
(b) b
(c) c
(d) d
Answer: (d)

Very Short Answer Type Questions 

Choose the correct answer from the given options:
 

Question. A pole of 6 m high casts a shadow \( 2\sqrt{3} \) m long, then sun’s elevation is
(a) 60°
(b) 45°
(c) 30°
(d) 90°
Answer: (a)

Question. At some time of the day, the length of the shadow of a tower is equal to height. Then the sun’s altitude at that time is
(a) 30°
(b) 60°
(c) 90°
(d) 45°
Answer: (d)

Question. The angle of depression of a car standing on the ground, from the top of a 75 m high tower is 30°. The distance of the car from the base of the tower (in m) is:
(a) \( 25\sqrt{3} \)
(b) \( 50\sqrt{3} \)
(c) \( 75\sqrt{3} \)
(d) 150
Answer: (c)

Assertion-Reason Type Questions

Question. Assertion (A): If the angle of elevation of Sun, above a perpendicular line (tower) decreases, then the shadow of tower increases.
Reason (R): It is due to decrease in slope of the line of sight.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (a)

Question. Assertion (A): When we move towards the object, angle of elevation decreases.
Reason (R): As we move towards the object, it subtends large angle at our eye than before.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer: (d)

Answer the following:

Question. A kite is attached to a string. Assuming that there is no slack in the string, find the height of the kite above the level of the ground, if the length of the string is 54 m and it makes an angle of 30° with the ground.
Answer: Let height be \( h \). \( \sin 30^\circ = \frac{h}{54} \Rightarrow \frac{1}{2} = \frac{h}{54} \Rightarrow h = 27 \) m.

Question. The ratio of the length of a vertical rod and the length of its shadow is \( 1 : \sqrt{3} \). Find the angle of elevation of the sun at that moment?
Answer: Let angle of elevation be \( \theta \). \( \tan \theta = \frac{1}{\sqrt{3}} \Rightarrow \theta = 30^\circ \).

Question. A tower stands vertically on the ground. From a point on the ground, which is 15m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.
Answer: Let height be \( h \). \( \tan 60^\circ = \frac{h}{15} \Rightarrow \sqrt{3} = \frac{h}{15} \Rightarrow h = 15\sqrt{3} \) m.