Answer:
Part 1) [tex]HI=15\ units [/tex]
Part 2) [tex]<G=61.93\°[/tex]
Part 3) [tex]< I=28.07\°[/tex]
The answer is the option A
Step-by-step explanation:
Part 1) Find the measure of side HI
Applying the Pythagoras Theorem
[tex]GI^{2} =GH^{2}+HI^{2}[/tex]
substitute the values and solve for HI
[tex]17^{2} =8^{2}+HI^{2}[/tex]
[tex]HI^{2}=17^{2}-8^{2}[/tex]
[tex]HI^{2}=225[/tex]
[tex]HI=15\ units [/tex]
Part 2) Find the measure of angle G
In the right triangle GHI
[tex]cos(G)=\frac{GH}{GI}[/tex]
substitute the values
[tex]cos(G)=\frac{8}{17}[/tex]
[tex]G=arccos(\frac{8}{17})=61.93\°[/tex]
Part 3) Find the measure of angle I
Remember that
The sum of the interior angles of a triangle must be equal to 180 degrees
so
[tex]<G+<H+<I=180\°[/tex]
substitute the values
[tex]61.93\°+90\°+< I=180\°[/tex]
[tex]< I=180\°-(61.93\°+90\°)=28.07\°[/tex]
