Answer:
c = 50
Step-by-step explanation:
We can use the Pythagorean Theorem to find the length of c in the given triangle. 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(shown below).
[tex]\fbox{\parbox{6cm}{\textbf{Pythagorean Theorem:}\[ c^2 = a^2 + b^2 \]Where:\\- $c$ represents the length of the hypotenuse.\\- $a$ represents the length of one of the legs.\\- $b$ represents the length of the other leg.\\}}[/tex]
In this problem:
[tex]\text{a = 48 , b = 14}[/tex]
(Note: you can switch them and it wouldn't change the answer)
Solving:
Plug in a and b into the Pythagorean Theorem:
[tex]\text{a}^{2} + \text{b}^{2} = \text{c}^2[/tex]
[tex]\text{48}^{2} + \text{14}^{2} = \text{c}^2[/tex]
[tex]2304 ~ + 196 = \text{c}^2[/tex]
[tex]\text{c} = \sqrt{2304+196}[/tex]
[tex]\text{c} = \sqrt{2500}[/tex]
[tex]\boxed{c = 50}[/tex]
Therefore, the length of "c" is 50.
