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When would you use the law of sines or law of cosines instead of a trigonometric ratio?
Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.
Law of cosines with a right angle?
The law of cosines with a right angle is just the pythagorean theorem. The cosine of 90 degrees is 0. That is why the hypotenuse squared is equal to the sum of both of the legs squared
Can the law of cosines be applied to right and non-right triangles?
Yes
How are all three versions of the law of cosines correct?
It follows from the cyclical symmetry of the cosine rule.
When and where was the law of cosines created?
Even though the cosine of an angle was not a known concept at the time, Euclid (3rd century BC) in Egypt stated and proved a pair of propositions which were equivalent to the law of cosines. One proposition was applicable for obtuse angles and the other to acute angles.
Who discovered the law of cosines?
A caveman from 10,000 BCal-Kashi was the 1st to provide an explicit statement of the law of cosines in a form suitable for triangulation
When would you use the law of sines or law of cosines instead of a trigonometric ratio?
Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.
How do you calculate the angles of a triangle knowing the sides?
Law of cosines
Law of cosines with a right angle?
The law of cosines with a right angle is just the pythagorean theorem. The cosine of 90 degrees is 0. That is why the hypotenuse squared is equal to the sum of both of the legs squared
When you have a right angle what does the law of cosines reduce to?
cosine = adjacent/hypotenuse
Can the law of cosines be applied to right and non-right triangles?
Yes
Can The law of cosines can only be applied to acute triangles?
No, it applies to all triangles.
What does the law of cosines reduce to when dealing with a right triangle?
D. The Pythagorean Theorem
Is it true that the law of cosines reduces the Pythagorean theorem with right triangles?
Yes
Can law of cosines can only be applied to acute triangles?
No, it applies to all triangles.
How are all three versions of the law of cosines correct?
It follows from the cyclical symmetry of the cosine rule.
When do you use the Law of Cosines?
We use the law of Cosines to be able to find : 1. The measure of the third side, when the measure of two sides and the included angle of a triangle ABC are known. 2. The measure of any angle, when the measure of the three sides of a triangle ABC are known.
