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 does the law of cosines work?

The Law of Cosines states: c2=a2+b2−2ab cosC . This resembles the Pythagorean Theorem except for the third term and if C is a right angle the third term equals 0 because the cosine of 90° is 0 and we get the Pythagorean Theorem.

Can you use law of cosines on right triangles?

You can ONLY use the Pythagorean Theorem when dealing with a right triangle. The law of cosines allows us to find angle (or side length) measurements for triangles other than right triangles. The third side in the example given would ONLY = 15 if the angle between the two sides was 90 degrees.

Is AAS law of cosines?

Therefore, the three angles are also named A, B, and C. The Law of Cosines states that: … An example of SSA is when you are given the sides c, and a, and angle C. An example of AAS is when you are given angles C and A, and side c.

Can you use the law of sines on any triangle?

The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. You will only ever need two parts of the Sine Rule formula, not all three.

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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.

What is 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). Another important relationship between the side lengths and the angles of a triangle is expressed by the Law of Cosines. …

Why is the Pythagorean theorem a special case of the law of cosines?

The Pythagorean Theorem is a special case of the law of cosines, a2 + b2 – 2*a*b*cos (theta) = c2 because cos (theta) = 0 when the angle is a 90 degree or right angle. We also learned that the converse of the Pythagorean Theorem is true as well.

How do you derive the law of cosines?


  1. Cosine function for triangle ADB. cosA=xc.
  2. x=ccosA.
  3. Pythagorean theorem for triangle ADB. x2+h2=c2.
  4. h2=c2−x2.
  5. Pythagorean theorem for triangle CDB. (b−x)2+h2=a2.
  6. Substitute h2 = c2 – x2 (b−x)2+(c2−x2)=a2.
  7. (b2−2bx+x2)+(c2−x2)=a2.
  8. b2−2bx+c2=a2.

Does law of sines work for obtuse angles?

The sine rule is also valid for obtuse-angled triangles. = for a triangle in which angle A is obtus. We can use the extended definition of the trigonometric functions to find the sine and cosine of the angles 0°, 90°, 180°. Draw a diagram showing the point on the unit circle at each of the above angles.

Can we use the law of sines in SSA case?

“SSA” is when we know two sides and an angle that is not the angle between the sides. use The Law of Sines first to calculate one of the other two angles; then use the three angles add to 180° to find the other angle; finally use The Law of Sines again to find the unknown side.

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Is SAS sine or cosine?

“SAS” is when we know two sides and the angle between them. use The Law of Cosines to calculate the unknown side, then use The Law of Sines to find the smaller of the other two angles, and then use the three angles add to 180° to find the last angle.

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