2022 · Q43
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 cos²A + cos²B + cos²C equal to?
Elementary MathematicsTrigonometry
- A3/4
- B1
- C5/4
- D2
Explanation
First test the sides: 9² + 12² = 81 + 144 = 225 = 15², so by the converse of Pythagoras, angle C is 90°. Then cos C = 0, and since A + B = 90°, cos B = sin A. So cos²A + cos²B + cos²C = cos²A + sin²A + 0 = 1. This identity holds for every right triangle, independent of the other angles. Hence option (B) 1.