Question

triangle pqr is similar to triangle xyz.
select all angles that have a cosine of \\( \frac { 9 } { 15 } \\).
\\( \square \angle p \\)
\\( \square \angle q \\)
\\( \square \angle r \\)
\\( \square \angle x \\)

Explanation:

Step1: Recall cosine formula in right - triangle

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Find \(\cos\) for angles in \(\triangle PQR\)

For \(\angle Q\) in \(\triangle PQR\), adjacent side to \(\angle Q\) is \(QR = 12\), hypotenuse \(PQ=15\), so \(\cos\angle Q=\frac{12}{15}\).
For \(\angle P\) in \(\triangle PQR\), adjacent side to \(\angle P\) is \(PR = 9\), hypotenuse \(PQ = 15\), so \(\cos\angle P=\frac{9}{15}\).
Since \(\triangle PQR\sim\triangle XYZ\), \(\angle X=\angle P\) (corresponding angles of similar triangles are equal). So \(\cos\angle X=\cos\angle P=\frac{9}{15}\)

Answer:

\(\angle P\), \(\angle X\)