2024 · Q56
Consider the following for the next two items that follow: ABC is a triangle right-angled at B. Given that AC − AB = 2 cm and BC = 16 cm. If ∠BAC = θ then what is sinθ + cosθ equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1
- B71/65
- C73/65
- D79/65
Explanation
Let AB = x; then AC = x+2, and Pythagoras gives x² + 16² = (x+2)². Expanding: x²+256 = x²+4x+4, so 4x = 252, x = 63 and AC = 65. With θ = ∠BAC, sinθ = 16/65 and cosθ = 63/65. Their sum is 79/65 — option D.