What do you use cosine for

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.

Law of Cosines The Law of Cosines is used to find the remaining parts of an oblique non-right triangle when either the lengths of two sides and the measure of the included angle is known SAS or the lengths of the three sides SSS are known. Subjects Near Me. Sides b and c are the other two sides, and angle A is the angle opposite side a.

These examples illustrate the decision-making process for a variety of triangles: e. We do know a side and its opposite angle. Therefore we use the Sine Rule. The question involves angles. Therefore we use trig ratios - sin, cos and tan. The question does not involve angles. Therefore we use Pythagoras's Theorem. We do not know a side and its opposite angle. Therefore we use the Cosine Rule. Find the unknown side or angle in each of the following diagrams: a.

Section 4: Sine And Cosine Rule Introduction This section will cover how to: Use the Sine Rule to find unknown sides and angles Use the Cosine Rule to find unknown sides and angles Combine trigonometry skills to solve problems Each topic is introduced with a theory section including examples and then some practice questions. At the end of the page there is an exercise where you can test your understanding of all the topics covered in this page.

You are allowed to use calculators in this topic. All answers should be given to 3 significant figures unless otherwise stated. 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. 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.

So now let's solve for a, because we know what bc and theta actually are. So a squared is going to be equal to b squared So, it's minus two, I'll just write it out. Minus two times 12 times nine, times the cosine of 87 degrees. And this is going to be equal to, let's see, this is minus, let's see, 12 times nine is Minus times the cosine of 87 degrees. Now, let's get our calculator out in order to approximate this. And remember, this is a squared.

Actually, before I get my calculator out, let's just solve for a. So a is just going to be the square root of this. So a is going to be equal to the square root It's going to be equal to the square root of that. So let me copy and paste it.

So a is going to be equal to the square root of that, which we can now use the calculator to figure out. Let me increase this radical a little bit, so that we make sure we're taking the square root of this whole thing. So let me get my calculator out.