## Related questions with answers

Question

Find the indicated sides of the right triangle. b = 5600, c = 6500, a = ?

Solutions

VerifiedSolution A

Solution B

Answered 2 years ago

Step 1

1 of 3In this problem, use the Pythagorean Theorem:

$c^2=a^2+b^2\tag{1}$

where $a$, $b$, and $c$ are the sides of the triangle.

Since the unknown value is $a$, rewrite the equation $\text{(1)}$ in terms of $a$ by subtracting $b^2$ on both sides of the equation.

$\begin{aligned} a^2&=c^2-b^2 \end{aligned}$

Step 1

1 of 2Pythagorean theorem: "in a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the length of the other two sides"

$\\c^2 = a^2 + b^2\\ b = 5600, c = 6500\\ 6500^2 = a^2 + 5600^2\\ a^2 = 6500^2 - 5600^2\\ a^2 = 42250000 - 31360000\\ a^2 = 10890000\\ a = \sqrt{ 10890000} \\ a =3300$

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