The angle measures of any triangle = 180
adding 27 and 63. = 90
leaving 90 degrees for the remaining angle
therefore the triangle is a right triangle
by definition if a triangle has a 90 degree angle it's a right triangle
Answer:
Part 1) ![HI=15\ units](https://tex.z-dn.net/?f=HI%3D15%5C%20units%20)
Part 2) ![](https://tex.z-dn.net/?f=%3CG%3D61.93%5C%C2%B0)
Part 3) ![< I=28.07\°](https://tex.z-dn.net/?f=%3C%20I%3D28.07%5C%C2%B0)
The answer is the option A
Step-by-step explanation:
Part 1) Find the measure of side HI
Applying the Pythagoras Theorem
![GI^{2} =GH^{2}+HI^{2}](https://tex.z-dn.net/?f=GI%5E%7B2%7D%20%3DGH%5E%7B2%7D%2BHI%5E%7B2%7D)
substitute the values and solve for HI
![17^{2} =8^{2}+HI^{2}](https://tex.z-dn.net/?f=17%5E%7B2%7D%20%3D8%5E%7B2%7D%2BHI%5E%7B2%7D)
![HI^{2}=17^{2}-8^{2}](https://tex.z-dn.net/?f=HI%5E%7B2%7D%3D17%5E%7B2%7D-8%5E%7B2%7D)
![HI^{2}=225](https://tex.z-dn.net/?f=HI%5E%7B2%7D%3D225)
![HI=15\ units](https://tex.z-dn.net/?f=HI%3D15%5C%20units%20)
Part 2) Find the measure of angle G
In the right triangle GHI
![cos(G)=\frac{GH}{GI}](https://tex.z-dn.net/?f=cos%28G%29%3D%5Cfrac%7BGH%7D%7BGI%7D)
substitute the values
![cos(G)=\frac{8}{17}](https://tex.z-dn.net/?f=cos%28G%29%3D%5Cfrac%7B8%7D%7B17%7D)
![G=arccos(\frac{8}{17})=61.93\°](https://tex.z-dn.net/?f=G%3Darccos%28%5Cfrac%7B8%7D%7B17%7D%29%3D61.93%5C%C2%B0)
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
![](https://tex.z-dn.net/?f=%3CG%2B%3CH%2B%3CI%3D180%5C%C2%B0)
substitute the values
![61.93\°+90\°+< I=180\°](https://tex.z-dn.net/?f=61.93%5C%C2%B0%2B90%5C%C2%B0%2B%3C%20I%3D180%5C%C2%B0)
![< I=180\°-(61.93\°+90\°)=28.07\°](https://tex.z-dn.net/?f=%3C%20I%3D180%5C%C2%B0-%2861.93%5C%C2%B0%2B90%5C%C2%B0%29%3D28.07%5C%C2%B0)
Answer:
B and C
Step-by-step explanation:
6*12 = 72ft²
The area of the trampoline is 72ft²
Hope this helps! :)
Step-by-step explanation:
1.solution
=2a+5a
=7a
2.solution
=12x-3x
=9x
3.solution
=3p+2p-p
=5p-p
=4p
Hope it helps you.