Trigonometry (Applications Case Study) (10 Mathematics)
Real-world applications of trigonometry involving heights, distances, angles of elevation and depression. CBSE-style case questions on surveying, engineeri
TL;DR: Real-world applications of trigonometry involving heights, distances, angles of elevation and depression. CBSE-style case questions on surveying, engi…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Real-world applications of trigonometry involving heights, distances, angles of elevation and depression. CBSE-style case questions on surveying, engineeri
Trigonometry (Applications Case Study) MCQs with Answers & Explanations
Q1. A boy stands 30 meters from the base of a tree and observes that the angle of elevation to the top is 45 degrees. What is the height of the tree?
- 15 m
- 30 m ✓ (correct)
- 30 sqrt(2) m
- 60 m
Q2. From the top of a building 80 meters tall, the angle of depression to a car on the ground is 30 degrees. How far is the car from the base of the building?
- 40 m
- 40 sqrt(3) m
- 80 sqrt(3) m ✓ (correct)
- 160 m
Q3. A ladder leans against a wall at an angle of 60 degrees with the ground. If the ladder is 10 meters long, what height on the wall does it reach?
- 5 m
- 5 sqrt(3) m ✓ (correct)
- 10 m
- 10 sqrt(3) m
Q4. A surveyor measures an angle of 60 degrees from point A to the top of a tower 100 meters away horizontally. Later, moving 50 meters closer (point B), the angle is now 75 degrees. This scenario best demonstrates which concept?
- Law of Sines
- Complementary angles
- Angle of elevation changes with distance ✓ (correct)
- Inverse trigonometric functions
Q5. An aeroplane at height 2000 meters observes the angle of depression to two buildings on opposite sides of a road at 30 degrees and 45 degrees respectively. If both angles are measured from the plane, what is the distance between the buildings?
- 2000 m
- 2000 + 2000 sqrt(3) m
- 2000 sqrt(3) + 2000 m ✓ (correct)
- 4000 m
Q6. In a right triangle, sin(A) = 3/5. What is cos(A)?
- 3/4
- 4/5 ✓ (correct)
- 4/3
- 5/4
Q7. A boy on top of a cliff 50 meters high observes a boat at angle of depression 45 degrees. Later, the boat comes closer and the angle of depression becomes 60 degrees. How far did the boat travel?
- 50(sqrt(3) - 1) m ✓ (correct)
- 50 m
- 50 sqrt(3) m
- 100 m
Q8. Two poles of heights 10 m and 20 m are 15 m apart. What is the angle of elevation from the top of the shorter pole to the top of the taller pole?
- 30 degrees
- tan^-1(2/3) ✓ (correct)
- 45 degrees
- 60 degrees
Frequently Asked Questions
What is the relationship between angle of elevation and angle of depression?
Angle of elevation is the angle above the horizontal when looking up at an object from a lower position. Angle of depression is the angle below the horizontal when looking down at an object from a higher position. For an observer at height h and object at horizontal distance d, the angle of elevation from the object to the observer equals the angle of depression from the observer to the object (alternate interior angles with respect to the horizontal).
How do we choose between sin, cos, and tan in trigonometry problems?
Identify which sides and angles are given and which are unknown. Use SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Choose the ratio containing the known angle, known side, and unknown side you need to find. In practical problems, first determine if you have the angle and can find opposite, adjacent, or hypotenuse.
More 10 Mathematics MCQs
- Coordinate Geometry
- Arithmetic Progressions
- Circles
- Surface Areas and Volumes
- Probability (Case Study)
- Coordinate Geometry (Case Study)
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →