Question

consider this right triangle. determine whether each expression can be used to find the length of side pq. select yes or no for each expression.

Explanation:

Step1: Use Pythagorean theorem

By Pythagorean theorem \(PQ=\sqrt{5^{2}+12^{2}} = 13\). Also, use trigonometric ratios. \(\sin P=\frac{12}{PQ}\), then \(PQ=\frac{12}{\sin P}\). \(\cos P=\frac{5}{PQ}\), so \(PQ=\frac{5}{\cos P}
eq\frac{12}{\cos P}\). \(\sin Q=\frac{5}{PQ}\), then \(PQ = \frac{5}{\sin Q}\). \(\tan Q=\frac{5}{12}\), and \(PQ
eq\frac{5}{\tan Q}\)

Answer:

Expression	Yes	No
\(\frac{12}{\cos(P)}\)		Yes
\(\frac{5}{\sin(Q)}\)	Yes
\(\frac{5}{\tan(Q)}\)		Yes