Question

Classify the following triangle as acute, right or obtuse. A triangle with side lengths of 12 in, 15 in, and 20 in. Explain why?

Answer 1

Assign:

Side `a = 12" in"`

Side `b = 15" in"`

Side `c = 20" in"`

`angle A` the angle opposite side a

`angle B` the angle opposite side b

`angle C` the angle opposite side C

End of the assignment section

One form of The Law of cosines is:

`c^2= a^2+ b^2-2(a)(b)cos(C)`

Substitute for the values of `a, b, and c`:

`20^2= 12^2+ 15^2-2(12)(15)cos(C)`

Solve for C (in degrees):

`cos(C) = (20^2-12^2-15^2)/(-2(12)(15))`

`C = cos^-1((20^2-12^2-15^2)/(-2(12)(15)))`

`C ~~ 94.9^@`

The triangle contains an angle that is greater than `90^@`, therefore, it is an obtuse triangle.