Up to this point, angles 1 and 2 have not been assigned an angular value. All that is known about the size of the angles is that they must have a sum of 90°. Remember, that the sum of all the angles must be 180°. Since one of the angles remains 90°, angles 1 and 2 comprise the difference (90°).

In Right Traingle Trigonometry - Part 2, the sine of angle 1, abbreviated sin1, was found to be 0.60. The 0.60 value correlates to an angular value of 36.87° (or 37°, rounded to the whole degree). This means that no matter the size of the triangle, angle 1 will remain a constant size provided sin1=0.60. In other words, if the ratio between the opposite side (of angle 1) and the hypotenuse remains 0.60 (6:10), the angle will remain 37°. The same value for angle 1 (37°) will be found using any of the three ratios, with respect to their individual trig function. By the way, the value of angle 1 is found by using the inverse trig functions on a calculator (be sure to review and understand the use of the calculator functions), or trig tables listing sine, cosine and tangent values. A trig table of whole degrees from 1 to 89 is located in Fig.2.

Now that angle 1 has been found, the solution for angle 2 can be found using the trig functions, or by simply subtracting the value of angle 1 from 90°. Angle 2 has a value of 53° (90°-37°).