2022 · Q44
Consider the following for the next two (02) items that follow: In triangle ABC, AB = 15 cm, BC = 9 cm and AC = 12 cm. What is sin²A + sin²B + sin²C equal to?
Elementary MathematicsTrigonometry
- A2
- B5/4
- C1
- D3/4
Explanation
sin²A+sin²B+sin²C = sin²A+cos²A+1 = 2 (since C = 90°). Equivalently, in any right triangle the squares of the sines of the three angles sum to 2. The keyed option is A.