Some Applications of Trigonometry — Flashcards
Karnataka Board · Class 10 · Mathematics
20 flashcards for Some Applications of Trigonometry (Karnataka Board Class 10 Mathematics) to test yourself on key terms and facts.
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A tower stands vertically on the ground. From a point 15 m away from the foot of the tower, the angle of elevation to the top is 60°. Find the height of the tower.
Answer
Step 1: Draw a right triangle with tower as height, ground distance as base Step 2: Identify known values: base = 15 m, angle = 60° Step 3: Use tan 60° = height/base Step 4: √3 = h/15 Step 5: h = 15√3…
An observer 1.5 m tall stands 28.5 m away from a chimney. The angle of elevation from her eyes to the top is 45°. Find the chimney's height.
Answer
Step 1: Total height = observer height + height above eye level Step 2: Eye level distance = 28.5 m, angle = 45° Step 3: Use tan 45° = height above eye level/distance Step 4: 1 = h/28.5, so h = 28.5 m…
A ladder 5 m long leans against a wall making an angle of 60° with the ground. How high up the wall does the ladder reach?
Answer
Step 1: Draw right triangle with ladder as hypotenuse Step 2: Given: hypotenuse = 5 m, angle with ground = 60° Step 3: Height = opposite side to 60° angle Step 4: Use sin 60° = height/hypotenuse Step …
From the top of a building 20 m high, the angle of depression to a car on the ground is 30°. Find the distance of the car from the base of the building.
Answer
Step 1: Angle of depression = angle of elevation from car to building top Step 2: Form right triangle: height = 20 m, angle = 30° Step 3: Use tan 30° = height/distance Step 4: 1/√3 = 20/d Step 5: d = …
A flag pole casts a shadow of 10 m when the sun's elevation is 45°. Find the height of the flag pole.
Answer
Step 1: Shadow length = base of right triangle = 10 m Step 2: Sun's elevation angle = 45° Step 3: Use tan 45° = height/shadow length Step 4: 1 = h/10 Step 5: h = 10 m Answer: Height of flag pole = 10 …
A tree breaks and bends so its top touches the ground 8 m from its base at an angle of 30°. Find the original height of the tree.
Answer
Step 1: Broken part forms hypotenuse of right triangle Step 2: Base = 8 m, angle with ground = 30° Step 3: Remaining height = 8 × tan 30° = 8/√3 m Step 4: Broken length = 8/cos 30° = 8/(√3/2) = 16/√3 …
When do you use the tangent ratio in height and distance problems?
Answer
Use tan θ when you have: - One angle (other than 90°) - One side adjacent to or opposite the angle - Need to find the other side (adjacent or opposite) Formula: tan θ = opposite/adjacent Example: If a…
A kite is flying at height 60 m. The string makes 60° with the ground. Find the length of string (assume no slack).
Answer
Step 1: String forms hypotenuse of right triangle Step 2: Height = 60 m, angle with ground = 60° Step 3: Use sin 60° = height/string length Step 4: √3/2 = 60/L Step 5: L = 60 × 2/√3 = 120/√3 = 40√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
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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