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# What Is the Law of Sines and Cosines?

**The law of sines and law of cosines are two different equations relating the measure of the angles of a triangle to the length of the sides.** The laws apply to any triangle, not just right-angled triangles.

Draw a triangle. Label the angles A, B and C and the opposite sides a, b and c. The law of sines says that the sines of the angles are proportional to the lengths of the opposite sides. That means sin A/a = sinB/b = sinC/c.

The law of cosines says that for any triangle, the square of the length of any side equals the sum of the squares of the other two sides minus 2 times the product of those two sides times the cosine of the included angle. If seeking the length of side a, for example, use the formula a^2 = b^2 + c^2 - (2bc cosA), and then take the square root of both sides of the equation.

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## What Is the Formula for the Law of Cosines?

A: The formula for the law of cosines is c^2 = a^2 + b^2 - 2ab x cos(C), where a, b and c are the sides of a triangle, and C is the angle opposite side c. The... Full Answer >Filed Under: -
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## When Was Trigonometry Invented?

A: Ancient Egyptian and Greek philosophers used an early form of trigonometry that involved calculating chords to obtain the angles of a triangle. This method... Full Answer >Filed Under: -
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## What Are the Side Lengths of an Isosceles Triangle?

A: An isosceles triangle has two side lengths that are equal and a remaining side that is of a different length. The two interior angles that are opposite the... Full Answer >Filed Under: -
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## How Do You Find the Tangent?

A: Find the tangent by dividing the length of the opposite side of a right triangle by the length of its adjacent side. The result of this equation is the tan... Full Answer >Filed Under: