In Triangle ABC, AC = BC and mC = 62°. The longest side of the triangle is:
AC
BC
AB
AM
Triangle is isosceles , so it is easy to find all the angles.
The longest side will always be opposite the largest angle.
The Answer is AB
To find the longest side of a triangle, we need to know the lengths of the sides. However, in this question, we are only given the angle measures and the fact that AC = BC.
Since AC = BC, we can conclude that the triangle is isosceles, meaning that two of its sides have equal lengths. Therefore, we can label the sides of the triangle as follows:
AC = BC
AB = BC (isosceles triangle property)
Now, let's analyze the angles. We are given that mC = 62°, which means angle C measures 62°. Since it is an isosceles triangle, angles A and B are also congruent.
Since the sum of the angles in a triangle is always 180°, we can solve for angles A and B:
Angle A + Angle B + Angle C = 180°
Angle A + Angle A + Angle C = 180° (isosceles triangle property)
2 * Angle A + 62° = 180°
2 * Angle A = 180° - 62°
2 * Angle A = 118°
Angle A = 118° / 2
Angle A = 59°
Therefore, angles A and B both measure 59° in this triangle.
Now, we can analyze the sides again. We know that AC = BC and AB = BC. Since AC and BC are the two equal sides, we can conclude that AC and BC are the shortest sides of the triangle.
So, the longest side of Triangle ABC is AB.