Answer:
- sin(θ) = 8/√113
- cos(θ) = 7/√113
- tan(θ) = 8/7
Explanation:
Given a right triangle with an acute angle marked θ next to a side marked 7 and opposite a side marked 8, you want the primary trig function values for angle θ.
Hypotenuse
The hypotenuse of the triangle can be found using the Pythagorean theorem:
c² = a² +b²
c² = 7² +8² = 113
c = √113 . . . . length of the hypotenuse
Trig functions
You are reminded of the side length ratios for the different trig functions by the mnemonic SOH CAH TOA.
Sin = Opposite/Hypotenuse
sin(θ) = 8/√113
Cos = Adjacent/Hypotenuse
cos(θ) = 7/√113
Tan = Opposite/Adjacent
tan(θ) = 8/7
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Additional comment
If you are required to "rationalize the denominator", then you need to replace 1/√113 with (√113)/113.
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