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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step-by-step explanation:

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simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .