Question

If m∠ A=65° m∠ B=15° m∠ C=100° , which lists the sides of the triangle in order from shortest to longest?

a. ‾BA‾AC ‾BC
b. ‾BA ‾BC ‾AC
c. ‾AC ‾BC ‾BA
d. ‾AC ‾AB ‾BC

Answer 1

In a triangle, sides are proportional to the angles opposite them. Thus, the side opposite the smallest angle is the shortest, and the one opposite the largest angle is the longest, so the side lengths from shortest to longest are ¬BA, ¬AC, ¬BC.

Step-by-step explanation:

To list the sides of the triangle in order from shortest to longest, we need to know that in a triangle, sides are proportional to the angles opposite them. This means that a larger angle will have a longer side opposite to it, and a smaller angle will have a shorter side opposite to it.

Since m∠ A=65°, m∠ B=15°, and m∠ C=100°, we know that the longest side will be opposite the largest angle, and the shortest side will be opposite the smallest angle. Therefore, side ¬BC (opposite angle A) will be shorter than side ¬AC (opposite angle B), and both will be shorter than side ¬BA (opposite angle C).

The correct order from shortest to longest side is: ¬BA, ¬AC, ¬BC. This corresponds to answer choice b. So, the give mcq answer in the final answer is b. ¬BA ¬BC ¬AC.