In a right-angled triangle, the two shorter sides measure 5 cm and 12 cm. What is the exact value of the sine of the smallest angle?
Answer and explanation
Correct answer: A. 5/13
- Step 1: Hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 cm. Step 2. The smallest angle faces the shortest side (5 cm). Step 3. Sine = opposite / hypotenuse = 5 / 13. Answer: 5/13. Why not the others: 12/13 is the cosine of the smallest angle (or sine of larger acute angle); 5/12 is the tangent; 12/5 is cotangent.
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