diff --git a/guide/english/mathematics/law-of-cosines/index.md b/guide/english/mathematics/law-of-cosines/index.md
index fbfa92dd0c..f545d2caf9 100644
--- a/guide/english/mathematics/law-of-cosines/index.md
+++ b/guide/english/mathematics/law-of-cosines/index.md
@@ -3,23 +3,47 @@ title: Law of Cosines
 ---
 ## Law of Cosines
 
-The Law of Cosines can be used to find the ramaining sides or angles of a non-right triangle when given either the length of two sides and its included angle (SAS) or the lengths of the three sides (SSS).
+The Law of Cosines can be used to find the remaining sides or angles of a non-right triangle when given either the length of two sides and its included angle (SAS) or the lengths of the three sides (SSS).
 The Law of Cosines states:
 <img src="http://hyperphysics.phy-astr.gsu.edu/hbase/imgmth/lcos.gif">
 
-This looks very similar to the Pythagorean Theorem, and if C was 90 degrees (a right triange), the expression acctually simplifies to the Pythagorean Thoerem.  So, the Pythagorean Theorem is a special case of the Law of Cosines.
+This looks very similar to the Pythagorean Theorem, and if C was 90 degrees (a right triange), then cos(C) = 0 and the expression simplifies to the Pythagorean Thoerem. So, the Pythagorean Theorem is a special case of the Law of Cosines.
 
-You can also switch the angle C with either A or B, but make sure to change the respective side (c) to a or b.
+You can also switch the angle C with either A or B, but need to change the respective side (c) to a or b:
 
-<img src="http://www.mathwarehouse.com/trigonometry/images/law-of-cosines/law-of-cosines-formula-and-picture2.png">
+<p align='center'>
+  a<sup>2</sup> = b<sup>2</sup> + c<sup>2</sup> - 2bc &middot; cos(A)<br />
+  b<sup>2</sup> = a<sup>2</sup> + c<sup>2</sup> - 2ac &middot; cos(B)<br />
+  c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup> - 2ab &middot; cos(C)
+</p>
 
-Ex:
+For example, suppose we have a triangle as above, with b = 21, c = 32 and A = 40&deg;. Then we can find the length of the remaining side a as well as the angles B and C using the cosine law.
 
-<img src="http://www.mathwarehouse.com/sheets/trigonometry/advanced/law-of-sines-and-cosines/images/picture-of-law-of-cosines.png">
-<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds  -->
+To start, let's find a. Since we know b, c and A, the first of the three formulas above will be best to use. We have
+
+<p align='center'>
+  a<sup>2</sup> = 21<sup>2</sup> + 32<sup>2</sup> - 2 &middot; 21 &middot 32 &middot; cos(40&deg;)
+</p>
+
+so simplifying and taking square roots we have a = sqrt(1465 - 1344 &middot; cos(40&deg;)) or approximately, a &approx; 20.87.
+
+Similarly, if we want to find the angle B, we now have the length of all three sides so the second formula above will be helpful. Rearranging we have
+
+<p align='center'>
+  cos(B) = [a<sup>2</sup> + c<sup>2</sup> - b<sup>2</sup>]/(2ac)
+</p>
+
+and so taking the inverse cosine (or arccosine) of both sides gives the angle B. Plugging in the lengths of our sides (using the exact expression for a found above, and only simplyfing at the end) we find B is approximately 40.31&deg;.
+
+Now to find C we have two approaches, either use the third formula above, or recall that the angles of our triangle should add up to 180 degrees, so if A is 40&deg; and B was found above, we have
+
+<p align='center'>
+  C = (180 - 40 - B)&deg; &approx; 99.69&deg;
+</p>
+
+(Checking with the cosine formula we get the same approximate answer, so we can rest easy knowing we haven't likely made a mistake in any of the calculations.)
 
 #### More Information:
 <!-- Please add any articles you think might be helpful to read before writing the article -->
-https://www.varsitytutors.com/hotmath/hotmath_help/topics/law-of-cosines
-http://mathworld.wolfram.com/LawofCosines.html
-
+- https://www.varsitytutors.com/hotmath/hotmath_help/topics/law-of-cosines
+- http://mathworld.wolfram.com/LawofCosines.html