Question

In a right triangle, two sides are 12 and 13. Find the measure of the third side. Consider all cases.

Answer 1

Answer: Approximately 17.69

Step-by-step explanation:

The formula needed to find the third side of this equation is the Pythagorean theorem. Which is as follows:

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

The difference between the two is that the first one after you do $a^2+b^2$ you still need to square root the answer you get to get the third side, aka. the hypotenuse. If you do the second method, you get the answer after you do the calculation which is a lot easier.

Below are the calculations needed to be made in both ways:

$12^2+13^2=313\\\sqrt{313}= 17.69$   17.69 was rounded to the hundredths place.

$\sqrt{12^2+13^2}=17.69$   once again this answer was rounded to the hundredths place.

$a^2+b^2$ are respectively for the sides of the triangles.

$c^2$ is respectively for the hypothenuse, which is the longest side, and across from the right angle (located by a box).

Answer 2

Answer:

5 or 17.69

Step-by-step explanation:

1st case senario:

c^2=a^2+b^2

c^2=12^2+13^2

c^2=144+169

c^2=313

c^2=$\sqrt{313}$

c=17.69

2nd case senario:

144+b^2=169

b^2=169-144

b^2=25

b^2=$\sqrt{25}$

b+5