To determine which side of triangle ABC is the longest, we need to find the actual measures of angles B and C first.
We know that the sum of the angles in a triangle is 180 degrees:
\[
\text{Measure angle A} + \text{Measure angle B} + \text{Measure angle C} = 180^\circ
\]
Given:
\[
\text{Measure angle A} = 60^\circ
\]
\[
\text{Measure angle B} = 3x - 2
\]
\[
\text{Measure angle C} = 2x + 7
\]
Using the angle sum property of the triangle:
\[
60 + (3x - 2) + (2x + 7) = 180
\]
Combine like terms:
\[
60 - 2 + 7 + 3x + 2x = 180
\]
\[
65 + 5x = 180
\]
Isolating \( x \):
\[
5x = 180 - 65
\]
\[
5x = 115
\]
\[
x = 23
\]
Now, substitute \( x = 23 \) back into the expressions for angles B and C:
\[
\text{Measure angle B} = 3x - 2 = 3(23) - 2 = 69 - 2 = 67^\circ
\]
\[
\text{Measure angle C} = 2x + 7 = 2(23) + 7 = 46 + 7 = 53^\circ
\]
Now we know the measures of the angles:
\[
\text{Measure angle A} = 60^\circ
\]
\[
\text{Measure angle B} = 67^\circ
\]
\[
\text{Measure angle C} = 53^\circ
\]
In a triangle, the longest side is opposite the largest angle. Here, the largest angle is \( \text{Measure angle B} = 67^\circ \).
Therefore, the side opposite angle B, which is side AC, is the longest side.
Side **AC** is the longest side.
Type the correct answer in the box.
In triangle ABC, which side is the longest if these are the measures of the angles?
measure angle A = 60 degrees, measure B = 3x-2 degrees, measure C = 2x + 7 degrees
Side ____ is the longest side.
1 answer
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