2022 · Q51
If A, B, C are acute angles and sin(B + C - A) = cos(C + A - B) = tan(A + B - C) = 1 then what is (A + B + C) equal to?
Elementary MathematicsTrigonometry
- A90°
- B120°
- C135°
- D150°
Explanation
sin(B+C-A) = 1 gives B+C-A = 90°; cos(C+A-B) = 1 gives C+A-B = 0°; tan(A+B-C) = 1 gives A+B-C = 45°. Solving yields C = 45°, A = 22.5°, B = 67.5°, summing to 135°. Hence the keyed option is C.