Question

A triangle has side lengths of 15 inches and 30 inches . It also has angles that' measure 45 and 20 . Witch of the following Identifies the possible third side length and third angle of the triangle

Answer 1

The third angle of the triangle is 115 degrees. The third side must be greater than 15 inches and less than 45 inches, based on the triangle inequality theorem.

Step-by-step explanation:

The subject of the question is finding the possible values for the third side length and third angle of a triangle. We know that a triangle is a three-sided figure lying on a plane with three angles that add up to 180 degrees.

Since two of the angles are given as 45 degrees and 20 degrees, we can find the third angle by subtracting the sum of these angles from 180 degrees:

Third angle = 180 - (45 + 20) = 180 - 65 = 115 degrees

To determine the possible length of the third side, the triangle inequality theorem should be considered, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. Given the side lengths of 15 inches and 30 inches:

The third side must be less than their sum: 15 + 30 = 45 inches

The third side must be more than their difference: 30 - 15 = 15 inches

Therefore, the possible range for the length of the third side is greater than 15 inches and less than 45 inches.

Answer 2

I think that it would be the third angle of the triangle because every triangle has to have 180 degrees in total for its angles.