Use the properties of triangles to find the third angle. For example, take an isosceles triangle with angles A, B and C where angles A and B equal 75 degrees and angle C is unknown. Because the angles of any triangle will equal 180 degrees, the unknown angle can be found by adding the two known angles together and subtracting the sum from 180. In this example, 180 = A + B + C = 75 + 75 + C = 150 + C. Subtract 150 from 180 to find that angle C equals 30 degrees.
Use the Law of Sines to find the remaining side. Using the example in Step 1, assume sides a and b equal 7 and side c is unknown. The Law of Sines states that a/sin A = b/sin B = c/sin C. Find side c by plugging in the values: 7/sin 75 = c/sin 30.
Multiple both sides by sin 30 to get: c = sin 30 * (7/sin 75). Use the calculator to solve: c = 0.5 * (7/0.966) = 0.5 * 7.246 = 3.623.
Use the Law of Sines to determine the remaining angles. Using the previous example, assume that angles A and B are unknown and angle C = 30 degrees. Sides a and b = 7 and side c = 3.623. Take the formula b/sin B = c/sin C.
Invert the fractions to get sin B/b = sin C/c. Plug in the values: sin B/7 = sin 30/3.623.
Multiply both sides by 7 to get sin B = (sin 30/3.623) * 7. Use the calculator to solve: sin B = (0.5/3.623) * 7 = 0.138 * 7 = 0.966.
Use the calculator to find the inverse sine: arcsin B = arcsin 0.966 = 75 degrees. Because angles A and B are equal, A = B = 75 degrees.