10 meters.
Step-by-step explanation:
To find the missing side of a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem is...
[tex]a^2+b^2=c^2[/tex]
Please be sure to note that a and b will always be the length of the sides and c will always be the hypotenuse, or in this case the ramp.
Since we know the values of both of the sides we can plug this into the theorem.
[tex]6^2+8^2=c^2[/tex]
Now we can solve.
[tex]36+64+c^2[/tex]
Add.
[tex]100=c^2[/tex]
Many people will make the mistake of thinking 100 is the final answer, but since c is squared we need to find the square root of 100.
[tex]\sqrt{100} =10[/tex]
c = 10
The ramp is 10 meters.
