Question

find the measure of the indicated angle. round your answer to the nearest tenth.

Explanation:

Step1: Apply the sine rule

The sine rule states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let the angle we need to find be \(A\), the side opposite to it \(a = 26\), and the hypotenuse \(c=33\) (assuming the right - angled triangle). Since it is a right - angled triangle, \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\).
\(\sin A=\frac{26}{33}\)

Step2: Calculate the angle

\(A=\sin^{- 1}(\frac{26}{33})\)
Using a calculator, \(A\approx52.3^{\circ}\)

Answer:

\(52.3^{\circ}\)