The Pythagorean theorem t is used to find missing side lengths in a right triangle. How do you solve for b, in terms of c and a?

Question

Savannah Anderson · Accepted Answer

#b = sqrt(c^2-a^2)# Given a right triangle with legs of length #a# and #b# and hypotenuse of length #c#, the Pythagorean theorem states that #a^2 + b^2 = c^2# Solving for #b#: #b^2 = c^2 - a^2# #=> b = +-sqrt(c^2-a^2)# However, we know that as a length, #b > 0#, so we can throw out the negative result. This leaves us with our answer: #b = sqrt(c^2-a^2)#

Abigail Allen · Answer

undefined To solve for the missing side length $ b $ in terms of the other two sides, $ a $ and $ c $, of a right triangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse ($ c $) is equal to the sum of the squares of the lengths of the other two sides ($ a $ and $ b $). Mathematically, it can be represented as:

$$ c^2 = a^2 + b^2 $$

To solve for $ b $, you need to isolate it on one side of the equation. Here's how:

$$ c^2 = a^2 + b^2 $$

$$ b^2 = c^2 - a^2 $$

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

Therefore, to find the length of side $ b $, you take the square root of the difference between the squares of the hypotenuse ($ c $) and the other side ($ a $).