a2 = b2 + c2 - 2 bc cos A

b2 = a2 + c2 - 2 ac cos B

c2 = b2 + a2- 2 ab cos C

If the given included angle is obtuse, remember that its cosine is negative and this sign must be applied

when the value of the cosine is substituted in the formula.

e. The tangent law states that the sum of any two sides of a triangle is to their difference as the

tangent of half the sum of their opposite angles is to the tangent of half the difference between their

opposite angles. This law is best suited for solving triangles in which two sides and the included angle

are given. The tangent law in equation form is as follows:

Since it is customary to avoid negative quantities when using the tangent law, you can rearrange the

equation to eliminate this. If in the equation above side a had been longer than side b, the equation

would have been as follows:

f. The half-tangent formulas are used to solve the angles of a triangle in cases where the given

information regarding the triangle is three sides. These formulas are as follows:

In the formulas above, s is equal to one-half the summation of the three sides (a, b, and c).

g. In the following paragraphs, there are some typical cases in which the above laws will help

you in determining the unknown quantities in oblique triangles.

side and two angles, find the value of the third angle by subtracting the sum of the two given angles

from 180. (The sum of the interior angles of a triangle equals 180.) Then, using the sine law, solve the

two unknown sides.

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