Given a right triangle with hypotenuse length $c$ and height $a$, which formula can be used to find the length of the base $b$?

• A. $b=a+c$
• B. $b=a^2+c^2$
• C. $b=\sqrt{c^2-a^2}$
• D. $b=\frac{c}{a}$

Answer: (C)

Verified step by step guidance

1. Recognize that the problem involves a right triangle with sides labeled as hypotenuse \( c \), height \( a \), and base \( b \). The hypotenuse is the longest side opposite the right angle.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: \( c^2 = a^2 + b^2 \).
3. To find the length of the base \( b \), rearrange the Pythagorean theorem to solve for \( b^2 \): \( b^2 = c^2 - a^2 \).
4. Take the square root of both sides to solve for \( b \): \( b = \sqrt{c^2 - a^2} \).
5. This formula allows you to calculate the base \( b \) when you know the hypotenuse \( c \) and the height \( a \) of the right triangle.