Question

the triangle below is a right triangle. use the pythagorean theorem to find the length of the hypotenuse. start by substituting the values you know and the value you dont know into the equation. use the variable c to represent the unknown side length. the pythagorean theorem says that if a, b, and c are the sides of a right triangle, where c is the hypotenuse, then: $a^2 + b^2 = c^2$. the right triangle has legs 3 and 4, and hypotenuse c. the equation to fill in is $\square^2 + \square^2 = \square^2$

Explanation:

Step1: Identify known sides

The right triangle has legs 3 and 4, hypotenuse \( c \).

Step2: Substitute into Pythagorean theorem

Using \( a = 3 \), \( b = 4 \), \( c = c \), substitute into \( a^2 + b^2 = c^2 \).
So \( 3^2 + 4^2 = c^2 \).

Answer:

\( 3 \), \( 4 \), \( c \) (in the respective boxes of \( a^2 + b^2 = c^2 \) as \( 3^2 + 4^2 = c^2 \))