What is law of sines

How do you use the law of sines?

How to Use the Law of Sines with a Triangle

  1. Using the law of sines and the proportion.
  2. fill in the values that you know. Use the given values, not those that you’ve determined yourself. …
  3. Use a calculator to determine the values of the sines (in this case, rounded to three decimal places).
  4. Multiply each side by the denominator under b to solve for that length.

What is the law of sines and when can it be used?

The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. … The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in scalene triangles, with the other being the law of cosines.

What is law of sines and cosines?

The Laws of Cosines and Sines. We saw in the section on oblique triangles that the law of cosines and the law of sines were useful in solving for parts of a triangle if certain other parts are known. … As usual, we’ll use a standard notation for the angles and sides of a triangle.

Can you use law of sines for SSS?

Use the law of cosines when you are given SAS, or SSS, quantities. For example: If you were given the lengths of sides b and c, and the measure of angle A, this would be SAS. SSS is when we know the lengths of the three sides a, b, and c. Use the law of sines when you are given ASA, SSA, or AAS.

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Where is angle of depression?

The angle of depression is the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, looking down at an object, you could measure the angle of depression.

Why does the law of sines work?

The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles . Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

What is law of cosines used for?

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. In the example in the video, the angle between the two sides is NOT 90 degrees; it’s 87.

Does law of sines work for all triangles?

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. You will need to know at least one pair of a side with its opposite angle to use the Sine Rule.

Who discovered the law of sines and cosines?

Johannes von Muller

Why does the law of sines not always work?

Cases when you can not use the Law of Sines

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Since we do not know an opposite side and angle, we cannot employ the formula. Or, just look at it: Remember when you have 2 sides, the angle must be non-included. By the way, we could use the law of cosines to find the length of the side opposite the 115° angle.

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.

Is Asa law of sines?

“ASA” is when we know two angles and a side between the angles. then use The Law of Sines to find each of the other two sides.

How do you solve SSS law of cosines?

To solve an SSS triangle:

  1. use The Law of Cosines first to calculate one of the angles.
  2. then use The Law of Cosines again to find another angle.
  3. and finally use angles of a triangle add to 180° to find the last angle.

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