Question

Classify each triangle by its angles and sides.
outside triangle
4.9
6
6.6
inside triangle
75 degrees
60 degrees
45 degrees


Question 2 options:

right isosceles


acute scalene


scalene isosceles


acute isosceles

Answer 1

To classify the triangles based on the information provided, we look at both the side lengths and the angles.

1. **Outside Triangle**:
- Side lengths: 4.9, 6, 6.6
- Since all side lengths are different, this triangle is classified as a **scalene triangle**.
- To determine the angle classification, we can compare the longest side (6.6) with the other sides:
- \(6.6^2 < 4.9^2 + 6^2\) (49.56 < 24.01 + 36), hence it is an acute triangle.
- Therefore, the outside triangle is classified as **acute scalene**.

2. **Inside Triangle**:
- Angles: 75 degrees, 60 degrees, 45 degrees
- All angles are less than 90 degrees, so this triangle is classified as an **acute triangle**.
- The angles are different, which means the triangle has no equal angles, therefore it is also scalene.
- As such, the inside triangle is classified as **acute scalene**.

Based on your options:
- The outside triangle corresponds to **acute scalene**.
- The inside triangle also corresponds to **acute scalene**.

Let me know if you have any further questions!