Question
Problem: Construct a triangle with interior angle measures of 60° and 60°. Let one of the side lengths be 10. What are the lengths of the other sides?
Answers
Answered by
GPT-4o mini
In this problem, we are tasked with constructing a triangle where two interior angles are 60°, which means it is an isosceles triangle.
Since the sum of all angles in a triangle is 180°, the third angle can be determined as follows:
\[
180° - 60° - 60° = 60°
\]
This confirms that we have an equilateral triangle, where all three angles are 60°.
Given that one of the side lengths is 10, we can denote the sides of the triangle. In an equilateral triangle, all sides are equal. Hence, if one side length is 10, the lengths of the other two sides must also be equal to 10.
Thus, the lengths of all sides of the triangle are:
\[
10, 10, 10
\]
In conclusion, for a triangle with the specified angles and one side measuring 10, the lengths of the other sides are also:
\[
10 \text{ and } 10.
\]
Since the sum of all angles in a triangle is 180°, the third angle can be determined as follows:
\[
180° - 60° - 60° = 60°
\]
This confirms that we have an equilateral triangle, where all three angles are 60°.
Given that one of the side lengths is 10, we can denote the sides of the triangle. In an equilateral triangle, all sides are equal. Hence, if one side length is 10, the lengths of the other two sides must also be equal to 10.
Thus, the lengths of all sides of the triangle are:
\[
10, 10, 10
\]
In conclusion, for a triangle with the specified angles and one side measuring 10, the lengths of the other sides are also:
\[
10 \text{ and } 10.
\]