In a triangle one of the angles is twice and the other is thrice the third angle. What is the ratio of the side opposite to the smallest angle to the side opposite to the largest angle?
Explanation:
The three angles of the triangle are in the ratio 1 : 2 : 3.
Hence, the given triangle can only be a 30°-60°-90° triangle.
Here, the side opposite the largest angle is the hypotenuse and the side opposite the smallest angle is the side opposite the angle with measure 30°.
Hence, by the 30°-60°-90° theorem
Side opposite to 30° angle is ½ of hypotenuse
∴ Ratio of the length of the largest side to the length of the smallest side is the ratio of the hypotenuse to the side opposite the angle with measure 30°
∴ (Side opposite to 30°)/Hypotenuse = 1/2
Hence, option (a).
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