Question

Consider AABC with the following measures:a = 5b = 12C = 90°Find c using Law of Cosines.(Here A is the angle opposite side a, B is the angle opposite side b, etc.)

Answer 1

Given: a=5

b=12

angle C =90 degrees

We have to find c using law of cosines.

The law of cosines is given by:

$c^2=a^2+b^2-2ab\cos (C)$

Putting the values,we have:

$\begin{gathered} c^2=5^2+12^2-2\times5\times12\times\cos (90^{\circ}) \\ =25+144-0 \end{gathered}$$c^2=169$

Taking squareroot we get :c=13 0r c=-13

But the side length can be a positive number so c=13.

The answer is c=13.