Properties Of Triangles — Flashcards
Telangana Open School (TOSS) · Class 12 · Mathematics
25 flashcards for Properties Of Triangles (Telangana Open School (TOSS) Class 12 Mathematics) to test yourself on key terms and facts.
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In triangle ABC, if a = 7, b = 5, and ∠C = 60°, find side c using the cosine rule.
Answer
Using cosine rule: c² = a² + b² - 2ab cos C Step 1: a = 7, b = 5, ∠C = 60°, cos 60° = 0.5 Step 2: c² = 7² + 5² - 2×7×5×0.5 = 49 + 25 - 35 = 39 Step 3: c = √39 ≈ 6.24 cm Answer: c ≈ 6.24 cm…
If in triangle ABC, a = 6, b = 8, and c = 10, find ∠C using the cosine formula.
Answer
Using cosine formula: cos C = (a² + b² - c²) / (2ab) Step 1: a = 6, b = 8, c = 10 Step 2: cos C = (36 + 64 - 100) / (2×6×8) = (100 - 100)/96 = 0/96 = 0 Step 3: cos C = 0 ⇒ ∠C = 90° Answer: ∠C = 90°…
In triangle ABC, ∠A = 45°, ∠B = 60°, and side a = 10 cm. Find side b using the sine rule.
Answer
Using sine rule: a/sin A = b/sin B Step 1: a = 10, ∠A = 45°, ∠B = 60° Step 2: 10 / sin 45° = b / sin 60° Step 3: sin 45° = √2/2 ≈ 0.707, sin 60° = √3/2 ≈ 0.866 Step 4: b = 10 × (0.866 / 0.707) ≈ 10 × …
The sides of a triangle are 5 cm, 7 cm, and 8 cm. Find the largest angle using the cosine rule.
Answer
Largest angle is opposite largest side (8 cm), so find ∠C. Using: cos C = (a² + b² - c²)/(2ab) Step 1: a = 5, b = 7, c = 8 Step 2: cos C = (25 + 49 - 64)/(2×5×7) = (74 - 64)/70 = 10/70 = 1/7 ≈ 0.1429 …
In triangle ABC, a = 4, b = 5, c = 6. Find cos A, cos B, and cos C.
Answer
Using cosine formulas: For cos A: (b² + c² - a²)/(2bc) = (25 + 36 - 16)/(2×5×6) = 45/60 = 0.75 For cos B: (a² + c² - b²)/(2ac) = (16 + 36 - 25)/(2×4×6) = 27/48 = 0.5625 For cos C: (a² + b² - c²)/(2ab)…
If in triangle ABC, a cos A = b cos B and a ≠ b, prove it is right-angled.
Answer
Given: a cos A = b cos B Using cos A = (b² + c² - a²)/(2bc), cos B = (c² + a² - b²)/(2ca) So: a×(b² + c² - a²)/(2bc) = b×(c² + a² - b²)/(2ca) Multiply both sides by 2c: a(b² + c² - a²)/b = b(c² + a² -…
In triangle ABC, a = 3, b = 4, c = 5. Find cos A, cos B, and cos C.
Answer
Using cosine formulas: cos A = (b² + c² - a²)/(2bc) = (16 + 25 - 9)/(2×4×5) = 32/40 = 0.8 cos B = (a² + c² - b²)/(2ac) = (9 + 25 - 16)/(2×3×5) = 18/30 = 0.6 cos C = (a² + b² - c²)/(2ab) = (9 + 16 - 25…
When do you use the sine rule?
Answer
Use the sine rule when: 1. Two angles and one side are known (AAS or ASA) 2. Two sides and a non-included angle are known (SSA) Example: In triangle ABC, ∠A = 30°, ∠B = 45°, a = 6 cm. Find b. Solution…
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