Question

the formula shown can be used to find the missing side length of a right triangle. a. which of the following represents the formula solved for a? a = c² - b², a = √(c² + b²), a = √(c² - b²). b. in a right triangle, side b = 6 inches and side c = 10 inches. find the length of side a.

Explanation:

Step1: Isolate $a^2$

Starting with $a^{2}+b^{2}=c^{2}$, subtract $b^{2}$ from both sides: $a^{2}=c^{2}-b^{2}$.

Step2: Solve for $a$

Take the square - root of both sides. Since $a$ represents a side - length (a non - negative quantity), $a = \sqrt{c^{2}-b^{2}}$.

Step3: Substitute values for part b

Given $b = 6$ and $c = 10$, substitute into $a=\sqrt{c^{2}-b^{2}}$. So $a=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8$.

Answer:

a. $a=\sqrt{c^{2}-b^{2}}$
b. 8 inches