Find the value of each variable. answer in simplest radical form.

x = 5√3; y = 5

Step-by-step explanation:

Finding y:  The sine function links the 30° angle, the 10 unit hypotenuse and the side opposite the angle, y:

sin 30° = 1/2 = y/10

Solve the equation of ratios

1        y

-- =  using cross-multiplication first:  2y = 10 → y = 5

2     10

We can now find x either by using a similar approach and the cosine function or by using the Pythagorean Theorem:

x² + y² = 10² = 100  →  x² = 100 - y²  =  100 - 5²  = 75

If x² = 75, then x = ±√75 = ± (√25)·(√3)   →  ±5√3

Since lengths are always positive,   take x = 5√3 as the answer.

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