Question

what is the measure of angle a in the triangle below? 30° 45° 60° 90°

Explanation:

Step1: Identify triangle type and sides

This is a right - triangle with right angle at \(C\). The hypotenuse \(AB = 18\) and the opposite side to angle \(A\), \(BC=9\). We can use the sine function, where \(\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Calculate \(\sin(A)\)

\(\sin(A)=\frac{BC}{AB}=\frac{9}{18}=\frac{1}{2}\)

Step3: Find the angle \(A\)

We know that if \(\sin(A)=\frac{1}{2}\), and \(A\) is an acute angle in a right - triangle (since the right angle is at \(C\)), then \(A = 30^{\circ}\) (because \(\sin(30^{\circ})=\frac{1}{2}\))

Answer:

\(30^{\circ}\)