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Use Law of Sines if you know:

  • Two angle measures and any side length or
  • Two side lengths and a non-included angle measure.

Use Law of Cosines if you know:

  • Two side lengths and the included angle measure or
  • Three side lengths.
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Q: When do you use law of sines and law of cos sines?
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When do you use law of sine?

There are several cases when you would want to use the law of sines. When you have angle angle side, angle side angle, or angle side side you would use the law of sines.


Proof of 30-60-90 theorem?

Use the law of sines.


Can you use the Law of Sines to find a missing angle measure in this triangular roof?

no #9


Describe the three situations when you can use the Law of Sines?

The tricky part of the law of sines is knowing when you are able to use it. Whether you can use the law of Sine's or not depends on what information you have or were given. In some cases the information you were given could make two different triangles. There are three times when you can use the law of sines. One example of when you can use it is when you have the length of a side and the measures of both the angles that that side is adjacent to. This is called angle side angle or asa for short. Another time when you can use the law of sines is when you are given the measures of two angles and a side that is outside the angles. This is called aas. Finally the last case where you can use the law of sines is when you have two side lengths and the measure of an angle. Math teachers refer to this one as ssa, I remember that this one is special. If you are given the measure of an angle and two sides you could have two different triangles.


How do you find the unknown angle of a triangle?

If you have two other angles, then add up those 2 and subtract that from 180. if you have all 3 sides then use the law of cosines: a squared = b squared + c squared - 2bc (cos A) If you have one angle and the 2 included sides, use the law of cosines as well. if you have an angle and the length of its opposite side, and the side opposite to the angle you want, then use the law of sines: sin A/ a = sin B/ b if you have the angle and the length of its opposite side and another angle, use the law of sines to figure out the unwanted angle anyway and then follow situation 1.


Does the transitive property apply for the law of sines?

No, it does not.


Why Lami's theorem cannot be used for 4 concurrent forces?

Because, this theorem comes from the law of sines which is completely a triangle law and the law of sines can not be applied on other polygons.


When can you use the sine law?

The tricky part of the law of sines is knowing when you are able to use it. Whether you can use the law of Sine's or not depends on what information you have or were given. In some cases the information you were given could make two different triangles. There are three times when you can use the law of sines. One example of when you can use it is when you have the length of a side and the measures of both the angles that that side is adjacent to. This is called angle side angle or asa for short. Another time when you can use the law of sines is when you are given the measures of two angles and a side that is outside the angles. This is called aas. Finally the last case where you can use the law of sines is when you have two side lengths and the measure of an angle. Math teachers refer to this one as ssa, I remember that this one is special. If you are given the measure of an angle and two sides you could have two different triangles.


How do you simplify csc theta -cot theta cos theta?

For a start, try converting everything to sines and cosines.


Can ASA work with the law of sines?

Yes. If you have two angles, by implication, you have all three. You therefore have a pair of opposite angle and side so that the law of sines can be applied.


How do you find the base of a triangle if is not given?

You use trigonometry. If the triangle is a right triangle, then you can use the Pythagorean theorem (a2 + b2 = c2 where c is the hypotenuse). This requires you to know two of the sides of the triangle. You can also use the relationship: sin A = a/c cos A = b/c tan A = a/b where "A" is a non-right angle of a right triangle, "a" is the length of the side opposite of the angle "A", "b" is the length of the side adjacent to the angle "A" and "c" is the length of the hypotenuse. If the triangle is NOT a right triangle, you can use the law of sines or the law of cosines. The law of sines: a /sin A = b / sin B = c / sin C where "a" is the side opposite of angle "A", "b" is the side opposite of angle "B" and "c" is the side opposite of angle "C". The law of cosines: a2 = b2 + c2 - b*c*cos A b2 = a2 + c2 - a*c*cos B c2 = a2 + b2 - a*b*cos C where "c" is the hypotenuse, "a" and "b" are the other sides of the triangle and "C" is the angle opposite of "c", "B" is the angle opposite of "b" and "A" is the angle opposite of "a".


How do you simplify tan ( - x ) cos ( - x )?

It helps, in this type of problem, to convert all trigonometric functions to sines and cosines. As a reminder, tan(x) = sin(x) / cos(x).