The hypotenuse and one of the legs of a right triangle form an angle that has a sine of 4/9 . what is the tangent of the angle? a) 4 (sq rt65)/65 b) 9(sq rt65)/65 c) (sq rt65)/4 d) (sq rt65)/9

A

Step-by-step explanation:

So by drawing a right triangle, and knowing that Sin of an angle is the opposite over hypotenuse, we know what two of the three sides are. Using the Pythagorean theorem, we know that 4^2+b^2 = 9^2. Since 16+ b^2 = 81, we can solve for be to get b^2 = 65, which means that the missing leg is the square root of 65. Tan of an angle is opposite over adjacent, or 4/square root 65. since square roots can not be in the denominator, multiply by the fraction sq. rt. 65/ sq. rt. 65. After you multiply, you should get the answer of 4(sq.rt. 65)/ 65  

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