Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together. For example, if the lengths of the sides measure 3 and 2, then squaring them would result in 9 and 4. Adding the squares together results in 13.

Square the length of the side opposite the obtuse angle. For the example, if the length is 4, then squaring it results in 16.

Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 16 subtracted from 13 equals -3.

Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 3 multiplied by 2 equals 6, and 6 multiplied by 2 equals 12.

Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -3 by 12, which results in -0.25.

Calculate the arc cosine of the value using your scientific calculator. The arc cosine, or arccos, is the inverse of the cosine value of the angle. Finding the arccos of the value will result in the measurement of the angle. Usually the arc cosine function will be found as the secondary function of the "cos" key. For the example, the arccos of -0.25 results in 104.4775 degrees. The obtuse angle has a measurement of 104.4775.

Repeat steps 1 through 6 using the other angles of the triangle.