Answer to Question #117463 in Trigonometry for Cecilia LeBrun

Question

Solve each triangle. Round answer to nearest tenth. Triangle RPQ angle P=18 degrees angle Q= 122 degrees r=25

Answer 1

Find te measure of the remaining angle: R=180^o-(P+Q)=180^o-(18^o+122^o)=40^o

Use the Law of Sines to find the missing side r measure: r/sin R=q/sin Q,

q=(r/sin R)*sin Q=(25/sin 40^o)*sin 122^o=(25/1.3)*0.8 $\approx$ 15.4

Similarly we can find side p by using the Law of Sines: p=(r/sin R)*sin P=(25/sin 40^o)*sin 18^o=(25/1.3)*0.3$\approx$ 5.8

Answer: R=40^o; q$\approx$ 15.4; p$\approx$ 5.8