Question

In triangle GHI, GH = 6, GI = 7, and m∠H = 64. To the nearest tenth, what is the m∠I?

Answer 1

50.4 degrees

Explanation:

Using sine rule

`\frac {HI}{sin<G}=\frac {GI}{sin<H}=\frac {GH}{sin<I}`

Therefore, to find angle I

`\frac {GI}{sin<H}=\frac {GH}{sin<I}`

Making angle I the subject of formula

`I=sin^(-1)(\frac {GH sin<H}{GI})`

Substituting GH = 6, GI = 7, and m∠H = 64

`I=sin^(-1)(\frac {6 sin64}{7})=50.389363496250\approx 50.39^(\circ)`

Therefore, angle I to the nearest tenth will be 50.4 degrees