Question

In △ABC, AB=9, BC=12, m∠B=90°, and m∠A=α.

What is sin⁡ α?

Enter your answer as a simplified fraction, like this: 3/14

Answer 1

`\text{Use the Pythagorean theorem:}\\\\AB^2+BC^2=AC^2\\\\AC^2=9^2+12^2\\\\AC^2=81+144\\\\AC^2=225\to AC=√(225)\\\\AC=15\\\\sine=(opposite)/(hypotenuse)\\\\\text{We have}\ opposite=12\ \text{and}\ hypotenuse=15.\ \text{Substitute:}\\\\\sin\alpha=(12)/(15)=(12:3)/(15:3)=(4)/(5)`