A triangle has side lengths of 15 inches and 30 inches. It also has angles that measure 45° and 20°. Which of the following identifies the possible third side length and third angle of the triangle?
So whats the answer T_T
C anyone? Formula a+b>c. Choose one side length in answer choices. I'm going to choose 17. 15(a)+17(b)=32. 32>30(c). its the only answer choice with 17 on it. if you didn't understand, look at the formula a+b>c 15 is a and 17 is b. 15+17 is 32 and you need a number greater than 30. C. 17, 115 degrees. if it is wrong I'm so sorry I got this question right when I did it, so IDK if teachers today use other techniques.
clearly the 3rd angle is 115°
Now look at the list of sides given. All you know is that the side lengths will be in the same order as the angle magnitudes: largest side opposite the largest angle.
With no diagram to look at, it's hard to say more.
To find the possible third side length and third angle of the triangle, we need to use the triangle inequality theorem and the fact that the sum of the angles in a triangle is always 180°.
First, let's use the triangle inequality theorem: In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
So, for the given side lengths of 15 inches and 30 inches:
- The third side length must be greater than the difference between the other two side lengths (30 - 15 = 15 inches) and less than the sum of the other two side lengths (30 + 15 = 45 inches).
Therefore, the possible third side length could be any value between 15 and 45 inches (exclusive).
Now let's find the possible third angle: The sum of the angles in a triangle is always 180°.
Given that one angle measures 45° and the other angle measures 20°:
- The third angle can be found by subtracting the sum of the other two angles (45° + 20° = 65°) from 180°.
- So, the third angle of the triangle is 180° - 65° = 115°.
Therefore, the possible third side length is between 15 and 45 inches (exclusive), and the possible third angle is 115°.