Question

classify each triangle by its angles and sides
Inside triangle
78 degree
62 degree
40 degree
Outside Triangle
2
3.1
2.8

is it
equilateral
obtuse isosceles
acute obtuse
acute scalene

Answer 1

To classify the triangles:

### Inside Triangle:
- Angles: 78 degrees, 62 degrees, and 40 degrees
- All angles are less than 90 degrees, which makes this triangle an **acute triangle**.
- Since all three angles are different, and thus all three sides must also be different, the triangle is classified as **acute scalene**.

### Outside Triangle:
- Side lengths: 2, 3.1, and 2.8
- Since all three side lengths are different, this triangle is classified as a **scalene triangle**.
- To find the angle classification, we can check the triangle inequality theorem to determine if it could potentially be obtuse or acute.

1. Calculate the square of the longest side (3.1):
\[
3.1^2 = 9.61
\]
2. Calculate the squares of the other two sides:
\[
2^2 + 2.8^2 = 4 + 7.84 = 11.84
\]
Since \( 9.61 < 11.84 \), the triangle’s angles are all less than 90 degrees. Therefore, the outside triangle is classified as an **acute scalene triangle**.

### Summary:
- Inside Triangle: **Acute Scalene**
- Outside Triangle: **Acute Scalene**