How to Solve Sine & Cosine in Triangles
A right triangle consists of one 90-degree angle, two shorter sides and a longer, slanted slide called the hypotenuse. The trigonometric functions sine, cosine and tangent are defined based on a right triangle. The functions rely on one of the two smaller angles. The shorter side closest to the angle in question is called "adjacent" while the furthest is called "opposite." Use a calculator to find the result of the trigonometric functions for specific angles.
Other People Are Reading
Instructions
-
Sine
-
1
Draw a right triangle with an additional angle of 35 degrees and the opposite side equal to 4. Use sine to find the hypotenuse of the triangle.
-
2
Use the following sine formula: sin(degrees) = opposite/hypotenuse or sin(35 degrees) = 4/h. Use your calculator to find sin(35 degrees) and round to the nearest hundredth: sin(35 degrees) = 0.57.
-
-
3
Plug that answer back into the formula: 0.57 = 4/h. Multiply both sides by "h": 0.57h = 4. Divide both sides by 0.57 and round to the nearest hundredth: h =7.02.
Cosine
-
4
Use cosine to find the adjacent side of a right triangle with a hypotenuse of 10 and an angle of 46. Note the cosine formula: cos(degrees) = adjacent / hypotenuse.
-
5
Plug the known quantities into the equation: cos (46 degrees) = a / 10. Solve "cos (46 degrees)" on your calculator, rounding the answer to the nearest hundredth: 0.69.
-
6
Place that answer into the formula: 0.69 = a / 10. Multiply both sides by 10: 6.9 = a.
-
1
