CBSE Class 10 Maths – MCQ and Online Tests – Unit 9 – Some Applications of Trigonometry
Every year CBSE conducts board exams for 10th standard. These exams are very competitive to all the students. So our website provides online tests for all the 10th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.
These online tests are based on latest CBSE Class 10 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.
CBSE Class 10 Maths – MCQ and Online Tests – Unit 9 – Some Applications of Trigonometry
Question 1.
If at some time, the length of the shadow of a tower is √3 times its height, then the angle of elevation of the sun, at that time is:
(a) 15°
(b) 30°
(c) 45°
(d) 60°
Answer
Answer: (b) 30°
Question 2.
A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is:
(a) 15√3 m
(b) \(\frac{15√3}{2}\) m
(c) \(\frac{15}{2}\) m
(d) 15 m
Answer
Answer: (c) \(\frac{15}{2}\) m
Question 3.
At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is:
(a) 30°
(b) 60°
(c) 90°
(d) 45°
Answer
Answer: (d) 45°
Question 4.
A person is flying a kite at a height of 30 m from the horizontal level. The length of string from the kite to the person is 60 m. Assuming that here is no slack in the string, the angle of elevation of kite to the horizontal level is:
(a) 45°
(b) 30°
(c) 60°
(d) 90°
Answer
Answer: (b) 30°
Question 5.
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 tower (in m) is:
(a) 25√3
(b) 50√3
(c) 75√3
(d) 150
Answer
Answer: (c) 75√3
Question 6.
A man at the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance travelled by the car during this time interval is:
(a) 10√3 m
(b) \(\frac{100√3}{3}\) m
(c) \(\frac{200√3}{3}\) m
(d) 200√3 m
Answer
Answer: (c) \(\frac{200√3}{3}\) m
Question 7.
The angle of elevation of the top of a 15 m high tower at a point 15 m away from the base of tower is:
(a) 30°
(b) 60°
(c) 45°
(d) 75°
Answer
Answer: (c) 45°
Question 8.
A man standing at a height 6 m observes the top of a tower and the foot of tower at angles of 45° and 30° of elevation and depression respectively. The height of tower is:
(a) 6√3 m
(b) 12 m
(c) 6(√3 – 1)
(d) 6(√3 + 1) m
Answer
Answer: (d) 6(√3 + 1) m
Question 9.
Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is:
(a) 5 m
(b) 8 m
(c) 9 m
(d) 10 m
Answer
Answer: (d) 10 m
Question 10.
A 6 feet tall man finds that the angle of elevation of a 24 feet high pillar and the angle of depression of its base are complementary angles. The distance of man from the pillar is:
(a) 4√3 feet
(b) 6√3 feet
(c) 8√3 feet
(d) 10√3 feet
Answer
Answer: (b) 6√3 feet
Question 11.
A lamp post 5√3 m high casts a shadow 5 m long on the ground. The sun’s elevation at this point is:
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer
Answer: (c) 60°
Question 12.
The angle of elevation of the top of a tower from a point P on the ground is α. After walking α distance d towards the foot of the tower, angle of elevation is found to be β. Then
(a) α < β
(b) α > β
(c) α = β
(d) None of these
Answer
Answer: (a) α < β
Question 13.
If the angles of elevation of the top of a tower from two points at the distance of 3 m and 12 m from the base of tower and in the same straight line with it are complementary, then the height of the tower (in m) is:
(a) 36
(b) 60
(c) 6
(d) 100
Answer
Answer: (c) 6
Question 14.
A ladder makes an angle of 60° with the ground, when placed along a wall. If the foot of ladder is 8 m away from the wall, the length of ladder is:
(a) 4 m
(b) 8 m
(c) 8√2 m
(d) 16 m
Answer
Answer: (d) 16 m
Question 15.
If the height and length of a shadow of a man are the same, then the angle of elevation of sun is:
(a) 30°
(b) 60°
(c) 45°
(d) 15°
Answer
Answer: (c) 45°
Question 16.
A bridge, in the shape of a straight path across a river, makes an angle of 60° with the width of the river. If the length of the bridge is 100 m, then the width of the river is:
(a) 50 m
(b) 173.2 m
(c) 43.3 m
(d) 100 m
Answer
Answer: (a) 50 m
Question 17.
The angle of elevation of the top of a tower from a point on the ground 30 m away from the foot is 30°. The height of the tower is:
(a) 30 m
(b) 10√3
(c) 20 m
(d) 10√2 m
Answer
Answer: (b) 10√3
Question 18.
The angle of elevation of the top of a tower at a distance of 500 m from the foot is 30°. The height of the tower is:
(a) 250√3 m
(b) 500√3 m
(c) \(\frac{500}{√3}\) m
(d) 250 m
Answer
Answer: (c) \(\frac{500}{√3}\) m
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