Question

pythagorean theorem proofs practice
complete this assessment to review what youve learned. it will not count toward your grade.
a right triangle has a leg length of 8 in. and a hypotenuse of length 10 in. what must be the length
of the other leg? (1 point)
check answer remaining attempts: 3

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown leg be \(a\), given one leg \(b = 8\) and hypotenuse \(c=10\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute values

Substitute \(b = 8\) and \(c = 10\) into \(a^{2}=c^{2}-b^{2}\). We get \(a^{2}=10^{2}-8^{2}=100 - 64=36\).

Step3: Solve for \(a\)

Take the square root of \(a^{2}=36\). Since \(a>0\) (length of a side), \(a=\sqrt{36}=6\).

Answer:

\(6\)