When the two non-right angles in a right triangle are of unknown value, you can use trigonometric functions to calculate them as long as you know the lengths of two of the three sides.
| You should look at a drawing of the triangle to anticipate the outcome of the calculation. Here is an example: in the diagram on the right, the angle q is smaller than 45o. We can also anticipate that the length y of the vertical side is larger than 1.0 cm and smaller than 2.5 cm. | |
We calculate q by using the sine function: sinq = (1.0/2.5) (the length units cancel out; the sine of an angle is just a pure number without units).
So sinq = 0.4. We aren't finished yet, of course; the sine of theta is not theta itself. We solve for theta using "arc-sine" or "inverse sine" of 0.4:
If you haven't used a calculator to do this kind of operation before, it generally works like this: while the display is showing the 0.4, press "2nd-F" (second function) or "INV" (inverse) followed by "sin". The answer should display as 23.6.
The unit of the answer is degrees as long as your calculator is set in the degrees mode. However, students (more often than you might think!) don't check to be sure that the angle unit on the calculator is set properly. You should make a habit of checking your calculator display: it should say "deg" or show the letter D somewhere rather than "rad" (radians of angle).
We might finish the problem by using the tangent function: