Question

determining missing components of right triangles. use the information given in the diagram of △ghi to find the missing measurements. round all answers to the nearest tenth. m∠g = 51°. hi =, gh =

Explanation:

Step1: Find HI using cosine function

We know that $\cos(I)=\frac{HI}{GI}$. Given $\angle I = 39^{\circ}$ and $GI = 30$. So $HI=GI\times\cos(I)=30\times\cos(39^{\circ})$. Using a calculator, $\cos(39^{\circ})\approx0.777$, then $HI = 30\times0.777 = 23.31\approx23.3$.

Step2: Find GH using sine function

We know that $\sin(I)=\frac{GH}{GI}$. Given $\angle I = 39^{\circ}$ and $GI = 30$. So $GH=GI\times\sin(I)=30\times\sin(39^{\circ})$. Using a calculator, $\sin(39^{\circ})\approx0.629$, then $GH = 30\times0.629 = 18.87\approx18.9$.

Answer:

$HI = 23.3$, $GH = 18.9$