FAQ: When to use the law of cosines?

How do you know when to use the law of sines or cosines?

The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

How is law of cosine used in real life?

The law of cosines is used in the real world by surveyors to find the missing side of a triangle, where the other two sides are known and the angle opposite the unknown side is known. To use the law of cosines formula, we simply plug in our two known sides into a and b, and then our angle into C.

When can cosine rule be used?

The Cosine Rule can be used in any triangle where you are trying to relate all three sides to one angle. If you need to find the length of a side, you need to know the other two sides and the opposite angle. Side a is the one you are trying to find.

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Does law of cosines work for right triangles?

In this case the tool is useful when you know two sides and their included angle. From that, you can use the Law of Cosines to find the third side. It works on any triangle, not just right triangles.

When can you not use the law of sines?

If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we cannot use the Law of Sines because we cannot set up any proportions where enough information is known.

How do you use the law of sines and cosines to solve a triangle?

This means we are given two sides and the included angle. For this type of triangle, we must use The Law of Cosines first to calculate the third side of the triangle; then we can use The Law of Sines to find one of the other two angles, and finally use Angles of a Triangle to find the last angle.

Is Pythagorean theorem only for right triangles?

Pythagorastheorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not. In the triangle above, if a 2 < b 2 + c 2 the angle is acute.

How do you remember the cosine rule?

You only need to remember the +2abcos(C) bit. Yep. It’s rearranged to resemble Pythagoras’s formula.

What are the law of sines and cosines?

The Law of Sines establishes a relationship between the angles and the side lengths of ΔABC: a/sin(A) = b/sin(B) = c/sin(C). This is a manifestation of the fact that cosine, unlike sine, changes its sign in the range 0° – 180° of valid angles of a triangle.

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What do you need to use the law of cosines?

When to Use

The Law of Cosines is useful for finding: the third side of a triangle when we know two sides and the angle between them (like the example above) the angles of a triangle when we know all three sides (as in the following example)

What does the law of cosines reduce to?

The Law of Cosines applies to any triangle with side lengths a,b,c and angles A,B,C. Note that if C is a right angle, then cos(C) = 0 and the law of cosines reduces to the Pythagorean Theorem: a2 + b2 = c2.

Which type of triangles does law of cosines work best on?

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.

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