8.1.2 Trigonometric Ratios (continued)
Example 2 Finding Trigonometric Ratios in Special Right Triangles
The tangent of the 30 ° angle of a special right triangle (30 ° -60 ° -90 ° ) is written as a fraction in this example. Recall that the lengths of the legs of a 30 ° -60 ° -90 ° right triangle are 1 and 3, and the length of the hypotenuse is 2. The tangent of an angle is the ratio of the length of the opposite side over the length of the adjacent side.
3
= = Tan 30 1 3
.
3
Example 3 Calculating Trigonometric Ratios
A calculator is used to calculate trigonometric ratios in this example. Make sure the calculator is set to calculate ratios for angles expressed in degrees and not radians. To calculate the cosine of 51 ° , enter 51 on the keypad and push the “cos” key. Round the result to the nearest hundredth as cos 51 ° ≈ 0.63. To calculate the sine of 29 ° , enter 29 and push the “sin” key. Express the result to the nearest hundredth as sin 29 ° ≈ 0.48. To calculate the tangent of 78 ° , enter 78 and push the “tan” key. Express the result to the nearest hundredth as tan 78 ° ≈ 4.70.
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