When do you use cosine law and sine law

The foot D of this perpendicular will lie on the edge BC of the triangle when both angles B and C are acute. Fortunately, the argument is the same in all three cases. Let h denote the length of this line AD, that is, the height or altitude of the triangle.

But this is true even when B is an obtuse angle as in the third diagram. There, angle ABC is obtuse. But the sine of an obtuse angle is the same as the sine of its supplement.

These two equations tell us that h equals both c sin B and b sin C. Since the three verions differ only in the labelling of the triangle, it is enough to verify one just one of them.

In case 2, angle C will be a right angle. In case 3, angle C will be acute. Case 1. For this case, we take angle C to be obtuse. 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. 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.

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If you need to find the length of a side, you need to use the version of the Sine Rule where the lengths are on the top:. Work out the length of x in the diagram below:. Start by writing out the Sine Rule formula for finding sides:.