which type of triangle has side measures of 5 cm, 9 cm, and 12.7 cm also one angle measure of 120
The given side lengths of 5 cm, 9 cm, and 12.7 cm, along with an angle measure of 120°, indicate that the triangle is an isosceles triangle.
An isosceles triangle has at least two sides of equal length. In this case, the side measures of 5 cm and 9 cm are not equal, so the triangle is not an equilateral triangle.
Now, let's check if the triangle is a right triangle.
Applying the Pythagorean theorem:
Let's assume that the side measures 5 cm and 9 cm are the equal sides of the triangle. The hypotenuse can be represented by side measure 12.7 cm.
Using the Pythagorean theorem, we have:
(5 cm)^2 + (9 cm)^2 = (12.7 cm)^2
25 cm^2 + 81 cm^2 = 161.29 cm^2
106 cm^2 ≠ 161.29 cm^2
Since the equation is not balanced, the triangle is not a right triangle.
Therefore, the triangle with side measures of 5 cm, 9 cm, and 12.7 cm, along with an angle measure of 120°, is an isosceles triangle.