How does cosine law work

So we need to know what this angle is as well. So let's say that we know that this angle, which we will call theta, is equal to 87 degrees.

So how can we figure out a? I encourage you to pause this and try this on your own. Well, lucky for us, we have the Law of Cosines, which gives us a way for determining a third side if we know two of the sides and the angle between them.

The Law of Cosines tells us that a squared is going to be equal b squared plus c squared. Now, if we were dealing with a pure right triangle, if this was 90 degrees, then a would be the hypotenuse, and we would be done, this would be the Pythagorean Theorem. But the Law of Cosines gives us an adjustment to the Pythagorean Theorem, so that we can do this for any arbitrary angle. So Law of Cosines tell us a squared is going to be b squared plus c squared, minus two times bc, times the cosine of theta.

And this theta is the angle that opens up to the side that we care about. So we can use theta because we're looking for a. If they gave us another angle right over here, that's not the angle that we would use. We care about the angle that opens up into the side that we are going to solve for. To find the other two angles, it is simplest to use the Law of Sines. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.

Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Varsity Tutors connects learners with experts. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. In this case, the foot D of this perpendicular will lie outside the triangle. Let h denote the height of the triangle, let d denote BD, and let e denote CD.

Case 2. Now consider the case when the angle at C is right. Case 3. In this case we assume that the angle C is an acute triangle. Formulae You Should Know You should already know each of the following formulae: formulae for right-angled triangles formulae for all triangles NOTE: The only formula above which is in the A Level Maths formula book is the one highlighted in yellow.

You must learn these formulae, and then try to complete this page without referring to the table above. Sine Rule The Sine Rule can be used in any triangle not just right-angled triangles where a side and its opposite angle are known.

Work out the answer to each question then click on the button marked. The triangle is not right-angled, and we don't know a side and its opposite angle, so we need to use the Cosine Rule. The triangle is right-angled, and the question involves angles, so we need to use trigonometric ratios.

The triangle is not right-angled, but we do know a side and its opposite angle, so we use the Sine Rule. The triangle is right-angled, but the question does not involve angles, so we need to use Pythagoras's Theorem. Work out the answers to the questions below and fill in the boxes. Click on the. Incorrect Answers There were 0 questions where you used the See solution button.

There were 0 questions where the answer was left incorrect. There were 0 questions which you didn't attempt or check. Since these pages are under development, we find any feedback extremely valuable.