Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

In a right triangle, with legs$a$ and $b$and hypotenuse$c$, the Pythagorean Theorem states that _________.

Step-by-Step Solution

Answer

In a right triangle, with legs$a$and $b$and hypotenuse$c$, the Pythagorean Theorem states that$c^2=a^2+b^2$.

Given information

In a right triangle, with legs $a$and $b$ and hypotenuse $c$, the Pythagorean Theorem states that _______________.

The main objective is to fill the blank with correct value.

Theorem:

According to the Pythagorean theorem, for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs of the triangles.

Here, the lengths of the two legs are $a$ and $b$ and the length of the hypotenuse is $c$.

Then by the Pythagorean theorem,

 $\begin{array}{rcl}{\mathrm{Hypotenuse}}^2& =& \mathrm{leg}{1}^2+\mathrm{leg}{2}^2\\ c^2& =& a^2+b^2\end{array}$

So, the blank will be filled with $c^2=a^2+b^2$.