Common Core: HSG-SRT.D.10
Law of Sines
Law of Sines: (sin A)/a = (sin B)/b = (sin C)/c
Proof: Law of Sines.
Trig: Law of Sines - The Derivation.
The Law of Sines
The Law of Sines is a relationship among the angles and sides of a
triangle. The ratio of the sine of any of the interior angles to the
length of the side opposite that angle is the same for all three
Law of Cosines
Law of Cosines: c2
The law of Cosines is a generalization of the Pythagorean Theorem.
If angle C were a right angle, the cosine of angle C would be zero
and the Pythagorean Theorem would result.
Law of cosines
A proof of the law of cosines using Pythagorean Theorem and algebra.
The Law of Cosines - Proof
This is a proof of the Law of Cosines that uses the xy-coordinate
plane and the distance formula. It does not introduce any letters
other than a, b, c, and ?. The idea is that we move a triangle such
that one of the sides rests on the x-axis; the formula comes from
algebraic manipulation after finding the length of the side opposite
the angle. It also works for any angle, so we don't have to do
tedious proofs for acute angles, obtuse angles, and angles greater
than 180 degrees.
sin? should be b2
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