SOLUTION: Using sohcahtoa: If Sin (α) = 1⁄2 what is the value of tan(α) ?

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Question 857707: Using sohcahtoa: If Sin (α) = 1⁄2 what is the value of tan(α) ?
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i'll use x instead of alpha.

sine(x) = opposite side divided by hypotenuse (SOH)

cosine(x) = adjacent side divided by hypotenuse (CAH)

tangent(x) = opposite side / adjacent side (TOA)

in your problem, sine (x) = 1/2

this means that the opposite side of angle x is equal to 1 and the hypotenuse is equal to 2.

by the pythagorean theorem:

the hypotenuse squared is equal to the side opposite the angle squared plus the side adjacent to the angle squared.

you can show this formula as:

h^2 = o^2 + a^2

you already know what the side opposite is and you know what the hypotenuse is by virtue of the fact that you know what the sine is and you know that the sine is opposite divided by hypotenuse.

replace h with 2 and o with 1 in the equation of h^2 = o^2 + a^2 to get:

2^2 = 1^2 + a^2

simplify to get:

4 = 1 + a^2

solve for a^2 to get a^2 = 3

solve for a to get a = sqrt(3)

you now know what all the sides of the triangle are.

side opposite is equal to 1
side adjacent is equal to sqrt(3)
hypotenuse is equal to 2

since the definition of tangent is side opposite divided by side adjacent, then tangent (x) is equal to 1 / sqrt(3).

that would be your answer if you didn't need to rationalize the denominator.

if you did need to rationalize the denominator, then you would multiply the numerator and denominator of 1 / sqrt(3) by sqrt(3) to get sqrt(3) / 3

your answer wouild then be:

tan(x) = sqrt(3)/3

a picture of your triangle is shown below:

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