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

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