Answer:
[tex]2\sqrt{13}[/tex]
Step-by-step explanation:
so that's a right triangle meaning there is a 90 degree angle (the red box inside of the triangle) in the triangle. when you have a right triangle, you can use the pythagoream theorm
pythagoream theorm = [tex]a^{2} + b^{2} = c^{2}[/tex]
- a and b are the two shortest sides of the triangle
- c is the longest side of the triangle, and it is always the side opposite of the right angle. we are trying to find c!
so a and b are given to us, which means...
a = 4
b = 6
PLUG IT IN!
[tex]4^{2} + 6^{2} = c^{2}[/tex] ----> you can simplify this to be
16 + 36 = [tex]c^{2}[/tex]
52 = [tex]c^{2}[/tex]
next, we have to isolate c in order to get the missing angle. this step is fairly simple as you just have to square both sides
[tex]\sqrt{52} = \sqrt{c^{2}}[/tex]
because 52 doesn't square nicely, you can just put it in your calculator to get about 7.2, or you can simplify it to be [tex]2\sqrt{13} = c[/tex] which will equal about 7.2 too if you put it in your calculator.
let me know if you have any questions!
