Answer:
x = 6 and y = 12
Step-by-step explanation:
30-60-90 Triangle Theorem
A special right-angled triangle where:
- Angles are in the ratio 1 : 2 : 3
- Sides are in the ratio 1 : √3 : 2
Therefore, the formula for the sides is b : b√3 : 2b where:
- b = shortest side opposite the 30° angle
- b√3 = side opposite the 60° angle
- 2b = longest side (hypotenuse) is opposite the right angle
The given triangle is a 30-60-90 triangle, therefore the ratio of its sides is b : b√3 : 2b
We have been given the measure of the side opposite the 60° angle.
⇒ b√3 = 6√3
So b = 6
Therefore, substituting the found value of b into the formula, the sides are in the ratio: 6 : 6√3 : 12
⇒ x = 6 (shortest side)
⇒ y = 12 (longest sides)
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