Question

determining an unknown angle measure of a right triangle
what is the measure of \\( \angle r \\) in \\( \triangle pqr \\)? round to the nearest degree.
\\( 26 ^ { \circ } \\)
\\( 42 ^ { \circ } \\)
\\( 45 ^ { \circ } \\)
\\( 64 ^ { \circ } \\)

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for angle \(R\), the adjacent side \(PR = 12.7\) and the hypotenuse \(QR=14.1\). We use the cosine ratio: \(\cos R=\frac{\text{adjacent}}{\text{hypotenuse}}\).
So, \(\cos R=\frac{12.7}{14.1}\).

Step2: Calculate the value of \(\cos R\)

\(\frac{12.7}{14.1}\approx0.8993\).

Step3: Find the angle \(R\)

We know that \(R = \cos^{-1}(0.8993)\).
Using a calculator, \(R\approx26^{\circ}\).

Answer:

\(26^{\circ}\)