Question

What is the length??

Answer 1

8.3

Explanation:

The equation to find the length of the hypotenuse from the legs is a² + b² = c². This means that you will need to square the lengths of the legs and then add them together to get the length of the hypotenuse squared. The lengths of the legs of this triangle are 2 and 8. 2 squared is 4, and 8 squared is 64. Add 64 + 4 to get 68. Now we know that 68 equals the hypotenuse squared. The square root of 68, 8.246, is the measurement of the hypotenuse. Now you just need to round up the number to the nearest tenth to get 8.3.

Answer 2

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{8} \end{cases} \\\\\\ c=√( 2^2 + 8^2)\implies c=√( 4 + 64 ) \implies c=√( 68 )\implies c\approx 8.2`