If tan (theta) is 5/12 and theta is an acute angle, find sin (theta)

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The tangent represents the sides making up the right angle in a right angle triangle. To find out the answer to what you have asked, the simplest way is to assume that you are talking about a right angle triangle.

Step One

Find the hypotenuse. Use a variation of the Pythagorean Theorem.

opposite^2 + adjacent^2 = hypotenuse^2

5^2 + 12^2 = x^2

25 + 144 = x^2

x^2 = 169

sqrt (x^2) = sqrt (169)

x = 13

Step Two

Find the sine.

When the tangent is given, the opposite in this case is 5.

That's because the opposite is always the numerator of a tangent.

Sin (theta) = 5/13 Answer