Properties Of Triangles
Telangana Open School (TOSS) · Class 12 · Mathematics
Flashcards for Properties Of Triangles — Telangana Open School (TOSS) Class 12 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
Interactive on Super Tutor
Studying Properties Of Triangles? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.
1,000+ Class 12 students started this chapter today
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…
+17 more flashcards available
Practice AllFrequently Asked Questions
What are the important topics in Properties Of Triangles for Telangana Open School (TOSS) Class 12 Mathematics?
How to score full marks in Properties Of Triangles — Telangana Open School (TOSS) Class 12 Mathematics?
How many flashcards are available for Properties Of Triangles?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Properties Of Triangles
Practice Quiz
Test yourself with a quick quiz
Important Questions
Practice with board exam-style questions
Revision Notes
Key points for last-minute revision
Formula Sheet
All formulas in one place
Chapter Summary
Understand the chapter at a glance
Concept Maps
See how topics connect visually
Study Plan
Step-by-step plan to ace this chapter
Syllabus
What topics to cover
NCERT Solutions
Every textbook question solved step by step
For serious students
Get the full Properties Of Triangles chapter — for free.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Telangana Open School (TOSS) Class 12 Mathematics.