Answer:
Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)
Step-by-step explanation:
The question doesn't specify which leg is under question. Is it the adacent leg or the opposite leg? I'll assume adjacent.
We can use the acronym
SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions. For an angle other than the right angle, the following relationships are defined.
SOH: S is sine = Opposite/Hypotenuse
CAH: C is cosine = Adjacent/Hypotenuse
TOA: T is tangent = Opposite/Adjacent
For a side adjacent (A) to the 36° angle, we can use
<u>Cosine = Adjacent/Hypotenuse</u>
Since we know the hypotenuse (12) we can find A:
Cosine(36) = A/12
A = Cosine(36)*12
A = (0.809)*12
<u>Adjacent = 9.71</u>
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If the opposite leg is calculated, we would use
Sine= Opposite/Hypotenuse
Sine(36) = Opposite/12
O = (0.5877)*12
<u>Opposite = 7.053</u>
