Answer:
Exact Value: [tex]\sqrt{28}[/tex]
Approximate Value: 5.29
Step-by-step explanation:
[] The Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex]
-> a and b are the legs of the triangle
-> c is the hypotenuse
[] We can plug in our known values, 6 and 8, then solve for UW.
-> Let 6 be a, UW be b, and 8 be c
[Given]
[tex]a^{2} +b^{2} =c^{2}[/tex]
[Plug-in]
[tex]6^{2} +b^{2} =8^{2}[/tex]
[Square 6 and 8]
[tex]36 +b^{2} =64[/tex]
[Subtract 36 from both sides]
[tex]b^{2} =28[/tex]
[Take the square root of both sides]
b = [tex]\sqrt{28}[/tex]
-> The square and square root "cancel each other out"
[] [tex]\sqrt{28}[/tex] is the exact value. The approximate value is 5.29 because the square root of 28 is equal to around 5.29
Have a nice day! Please keep in mind they may be looking for something different with regards to the exact/approximate values, but hopefully you can figure it out with the answer I have given.
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
