This page assumes that you have a basic understanding of
how to use law of cosines formula, and this page focuses
solely on the law of cosines (no law of sines problems on this page)

Practice Problems

Problem 1

Use the law of cosines to calculate the measure of $$\angle B $$

Don't let the $$ 29 ^{\circ }$$ angle fool you.

Remember: you can only use an angle when you are trying to solve for the 3rd side
of a triangle! The $$ 29^ \circ $$ does nothing for the law
of cosines. (As an aside, you could use that angle with the
law of sines
.)
You can even
cross it out
, if you want.

Use the law of cosines to find the length of side C

Don't let the $$ 53 ^{\circ}$$ angle fool you.

Remember:
the law of cosines requires the use of the included angle. The
$$ 53^ \circ $$ does nothing for you. ( Unless you know the
law of sines.)
You can even
cross it out
, if you want.

Step 1

Determine the appropriate form of formula

Since we want to find side c we need
$$
{\color{red}{c}}^2 = a^2 + b^2 -2ab \cdot cos(C)
\\
$$

Use the law of cosines to find the length of side A

Don't let the $$ 22 ^{\circ}$$ angle fool you.

Remember: you can only use an angle when you are trying to solve for the 3rd side
of a triangle! The $$ 22^ \circ $$ does nothing for you. (
Unless you know the
law of sines.)
You can even
cross
it out
, if you want.

Step 1

Determine the appropriate form of formula

Since we want to find side c we need
$$
{\color{red}{a}}^2 = b^2 + c^2 -2bc \cdot cos( A )
$$

For $$ \triangle EDF $$, find the length of side f, given that
$$ \angle E = 33 ^\circ, \angle F = 121^ \circ $$,d = 4
and e = 5. Round your answer to the nearest thousandth.

For word problems, the best thing to do, first and foremost, is draw a diagram.

Step 1

Draw picture

There are actually many ways to draw this triangle, but one version of the diagram is: