Some Applications of Trigonometry
Karnataka Board · Class 10 · Mathematics
Most important questions from Some Applications of Trigonometry for Karnataka Board Class 10 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Sample Questions
A man 1.8 m tall casts a shadow of 1.8 m. What is the angle of elevation of the sun?
Show answer
45°
Step 1: Height = 1.8 m, shadow = 1.8 m, angle of elevation = ? Step 2: tan(angle) = height/shadow = 1.8/1.8 = 1. Step 3: We know tan 45° = 1. Step 4: Therefore, angle of elevation = 45°.
From the top of a 60 m high building, the angle of depression of a car on the road is 30°. How far is the car from the building?
Show answer
60√3 m
Step 1: Building height = 60 m, angle of depression = 30°, horizontal distance = ? Step 2: Angle of depression equals angle of elevation from car to top. Step 3: tan 30° = height/distance = 60/distance. Step 4: 1/√3 = 60/distance, so distance = 60√3 m.
A tree breaks and bends to touch the ground 12 m away from its base, making 30° with the ground. What was the original height of the tree?
Show answer
8 + 4√3 m
Step 1: Let broken part length = l, standing part = h. Distance from base = 12 m, angle = 30°. Step 2: In right triangle: cos 30° = 12/l, so √3/2 = 12/l, giving l = 24/√3 = 8√3 m. Step 3: sin 30° = h/l, so 1/2 = h/(8√3), giving h = 4√3 m. Step 4: Original height = h + l = 4√3 + 8√3 = 12√3 m. Wait, let me recalculate. Step 2: sin 30° = h/l = 1/2, and cos 30° = 12/l = √3/2. Step 3: From cos equation: l = 12/(√3/2) = 24/√3 = 8√3 m. Step 4: From sin equation: h = l/2 = 4√3 m. Actually, let me be more careful. The standing part is h, broken part makes hypotenuse l. We have base = 12, angle = 30°. S
An airplane flying at 3000 m height observes the angle of depression of an airport to be 30°. What is the horizontal distance from the plane to the airport?
Show answer
3000√3 m
Step 1: Height = 3000 m, angle of depression = 30°, horizontal distance = ? Step 2: tan 30° = height/horizontal distance = 3000/distance. Step 3: 1/√3 = 3000/distance. Step 4: distance = 3000√3 m.
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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