Class 10 Some Applications of Trigonometry — practice questions with answers
Trigonometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. A ladder is leaning against a wall. The foot of the ladder is 3 meters away from the wall, and the ladder makes an angle of 60 degrees with the ground. Find the length of the ladder.
A6 meters
B1.5 meters
C5.20 meters
D3.46 meters
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Answer: A) 6 meters
Using the cosine ratio, cos(60∘)=length3. Therefore, length = 0.53=6 meters.
2. A person is standing on a hill 30 meters high. They see a car on the ground at an angle of depression of 30 degrees. Find the distance of the car from the base of the hill.
A51.96 meters
B17.32 meters
C30 meters
D60 meters
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Answer: A) 51.96 meters
Using the tangent ratio, tan(30∘)=distance30. Therefore, distance = tan(30∘)30=30×3≈51.96 meters.
3. A kite is flying at a height of 90 meters above the ground. The string attached to the kite is inclined at 60 degrees to the horizontal. Assuming there is no slack, find the length of the string (use 3 = 1.73).
Athe straight line drawn from the observer's eye to the object being viewed
Bthe horizontal line on the ground
Cthe vertical height of the object
Dthe shadow cast by the object
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Answer: A) the straight line drawn from the observer's eye to the object being viewed
The line of sight is the straight line joining the observer's eye to the point or object being observed; it forms the hypotenuse of the right triangle in such problems.
5. A ramp rises to a platform 2 meters high. If the ramp makes an angle of 30 degrees with the ground, find the length of the ramp (the sloping surface).
A8
B5
C3
D4
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Answer: D) 4
The ramp is the hypotenuse. sin(30 degrees) = 2 / ramp, and sin(30) = 0.5, so ramp = 2 / 0.5 = 4 meters.