2017 · Q46
If a triangle has sides 5, 13 and 12 units and θ is the acute angle of the triangle, then what is the value of (sin θ + cos θ) ?
Elementary MathematicsTrigonometry
- A5/13
- B7/13
- C12/13
- D17/13
Explanation
5²+12² = 13², so the triangle is right-angled. For either acute angle θ, {sin θ, cos θ} = {5/13, 12/13} in some order, so sin θ+cos θ = 17/13 whichever acute angle is meant. Hence option (D) 17/13.