Question

use the figure below to answer the following questions. round your answers to two decimal places. enter deg after any degree values.
a) what is ( mangle q )?
b) what is ( pr )?
c) what is ( pq )?

Explanation:

Part a) Step1: Recall triangle angle sum

In a right triangle, the sum of angles is \(180^\circ\), and one angle is \(90^\circ\) (right angle at \(R\)), another is \(44^\circ\) at \(P\). So \(m\angle Q = 180^\circ - 90^\circ - 44^\circ\).
\(m\angle Q = 46.00^\circ\)

Part b) Step1: Identify trigonometric ratio

In right triangle \(PRQ\), \(\tan(P)=\frac{QR}{PR}\), \(QR = 44\), \(P = 44^\circ\). So \(PR=\frac{QR}{\tan(44^\circ)}\).
\(\tan(44^\circ)\approx0.9657\), \(PR=\frac{44}{0.9657}\approx45.56\)

Part c) Step1: Identify trigonometric ratio

\(\sin(P)=\frac{QR}{PQ}\), so \(PQ=\frac{QR}{\sin(44^\circ)}\).
\(\sin(44^\circ)\approx0.6947\), \(PQ=\frac{44}{0.6947}\approx63.34\)

Answer:

a) \(46.00\) deg
b) \(45.56\)
c) \(63.34\)