Trigonometry in the Right Triangle · Ages 15–16
Finding Sine, Cosine, and Tangent in Right Triangles
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Use the side lengths given for each right triangle to write the trigonometric ratios as simplified fractions and decimals. Ensure your calculator is set to degree mode when calculating values.
A right triangle has legs of length 6 and 8, and a hypotenuse of 10. For the angle opposite side 6, find the sine ratio.
Using the same triangle, find the cosine ratio for the angle opposite side 6.
Using the same triangle, find the tangent ratio for the angle opposite side 6.
A right triangle has sides of 5, 12, and 13. For the angle opposite side 12, find the sine and cosine ratios.
For the same triangle (sides 5, 12, 13), find the tangent ratio for the angle opposite side 12.
A student calculates the cosine of an acute angle as 1.35. Explain why this result must be an error.
Using a calculator set to degree mode, find the value of sin(30°) and cos(60°).
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A right triangle has legs of length 6 and 8, and a hypotenuse of 10. For the angle opposite side 6, find the sine ratio.
6/10 or 3/5 (0.6)
Using the same triangle, find the cosine ratio for the angle opposite side 6.
8/10 or 4/5 (0.8)
Using the same triangle, find the tangent ratio for the angle opposite side 6.
6/8 or 3/4 (0.75)
A right triangle has sides of 5, 12, and 13. For the angle opposite side 12, find the sine and cosine ratios.
sin = 12/13 (approx. 0.923); cos = 5/13 (approx. 0.385)
For the same triangle (sides 5, 12, 13), find the tangent ratio for the angle opposite side 12.
12/5 (2.4)
A student calculates the cosine of an acute angle as 1.35. Explain why this result must be an error.
Cosine is the adjacent side divided by the hypotenuse. Because the hypotenuse is always the longest side in a right triangle, cosine cannot be greater than 1.
Using a calculator set to degree mode, find the value of sin(30°) and cos(60°).
sin(30°) = 0.5 and cos(60°) = 0.5