Solution

Regardless of orientation, you should be able to identify that the Hypotenuse of this right triangle is 14 cm and the given angle is \(\frac{2\pi}{9}\). The missing sides are the Opposite and Adjacent, so we will need to use the Sine (Opp/Hyp) and Cosine (Adj/Hyp) to solve the missing sides: \[ \solve{ \sin\left(\frac{2\pi}{9}\right)&=&\frac{Opp}{14}\\ Opp&=&14\sin\left(\frac{2\pi}{9}\right)\\ Opp&\approx&9 } \]\[ \solve{ \cos\left(\frac{2\pi}{9}\right)&=&\frac{Adj}{14}\\ Adj&=&14\cos\left(\frac{2\pi}{9}\right)\\ Adj&\approx&10.72 }\] Depending on how the question is asked, you may be required to give an exact answer (such as \(14\sin\left(\frac{2\pi}{9}\right)\) ) or approximate (such as 10.72). Make sure you check your directions in WebAssign. If no directions are provided, the best answer is the exact answer.