Question

multiple choice
question 9
listen
classify this triangle as specifically as possible.
(image of a triangle with angles 100°, 35°, and side lengths 7 in, 4 in, 8 in)

Explanation:

Step1: Analyze angle types

First, check the angles. One angle is \(100^\circ\) (obtuse, since it's greater than \(90^\circ\) and less than \(180^\circ\)). The other angles are \(35^\circ\) and we can find the third angle: \(180 - 100 - 35 = 45^\circ\) (all angles are different, so no equal angles).

Step2: Analyze side lengths

The side lengths are \(4\) in, \(7\) in, and \(8\) in. All side lengths are different (since \(4
eq7
eq8\)).

Step3: Classify the triangle

A triangle with one obtuse angle (greater than \(90^\circ\)) and all sides of different lengths is called an obtuse scalene triangle. Obtuse because of the \(100^\circ\) angle, scalene because all sides (and thus all angles) are of different measures.

Answer:

Obtuse Scalene Triangle