Answer:
x = 5√3; y = 5
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.