Question

Use the Pythagorean theorem to find b.

b, 13, 12

b =

Answer 1

5

Explanation:

a^2 + b^2 = c^2

13 is the hypotenuse because it is the longest side.

12^2 + b^2 = 13^2

144 + b^2 = 169

subtract the 144 from both sides to isolate the variable you are solving for

b^2 = 25

Square root both sides to solve

b = 5

Answer 2

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2-a^2)=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{12}\\ b=opposite\\ \end{cases} \\\\\\ √(13^2-12^2)=b\implies √(25)=b\implies 5=b`