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Two angles of a triangle measure 30° and 60°. Which of the following is true of the sides opposite these angles?

a) The side opposite the 30° angle is longer than the side opposite the 60° angle.
b) The side opposite the 60° angle is longer than the side opposite the 30° angle.
c) The sides opposite the 60° angle is twice as long as the side opposite the 30°.
d) There is no way to compare the sides opposite the angles.

User AbdulMueed
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Final answer:

In a triangle, the side opposite the larger angle is longer. In this case, the side opposite the 60° angle is longer than the side opposite the 30° angle, which is the correct answer to the question.

Step-by-step explanation:

When considering the relationships within a triangle, it's important to understand that the lengths of the sides are directly related to the angles opposite them. In a triangle, the larger the angle, the longer the side opposite that angle. You already know that the sum of angles in a triangle is 180 degrees, and in this particular triangle, you have angles measuring 30° and 60°, with the third angle necessarily being 90° since the angles must sum to 180°. Thus, you have a 30°-60°-90° triangle.

In a 30°-60°-90° triangle, the hypotenuse is opposite the 90° angle, the longest side is opposite the 60° angle, and the shortest side is opposite the 30° angle. This means that the correct answer is b) The side opposite the 60° angle is longer than the side opposite the 30° angle. It is a basic principle that the larger the angle, the longer the side opposite it. Therefore, it is not accurate to say the side opposite the 30° angle is longer, that the side is twice as long, or that there is no way to compare sides based on angles.

User LocalPCGuy
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