Trigonometry & Inverse Trigonometry
Properties of Triangles
Grade 11
Question:
<p>In a triangle ABC, if <span class='latex'>a^2 + b^2 + c^2 = \sqrt{2}b(c + a)</span>, then the triangle is:</p>
Step-by-Step Solution
Key Concept: Use the cosine rule and algebraic manipulation to determine the angle relationships.
<p><strong>Analysis:</strong> Given: <span class='latex'>a^2 + b^2 + c^2 = \sqrt{2}b(c + a)</span></p><p>Rearrange: <span class='latex'>a^2 + b^2 + c^2 = \sqrt{2}bc + \sqrt{2}ab</span></p><p>This suggests using the cosine rule: <span class='latex'>b^2 = a^2 + c^2 - 2ac\cos B</span></p><p>Through algebraic manipulation and using the constraint, we can show that angle B = 90°, making the triangle right-angled.</p><p>∴ Answer is (q) ΔABC is right angled triangle</p>
Correct Answer: q