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*5*12*\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.