Question

classify each triangle as acute, right, or obtuse.
48.5, 39, 32,5

Answer 1

those are the side lengths

Answer 2

To classify the triangle with angles 48.5°, 39°, and 32.5°, we need to determine whether the triangle is acute, right, or obtuse based on its angle measures:

1. **Acute Triangle**: All three angles are less than 90°.
2. **Right Triangle**: One angle is exactly 90°.
3. **Obtuse Triangle**: One angle is greater than 90°.

Now, let's analyze the angles given:

- 48.5° (which is less than 90°)
- 39° (which is less than 90°)
- 32.5° (which is also less than 90°)

Since all three angles are less than 90°, this triangle is classified as an **acute triangle**.

Answer 3

Thank you for the clarification! If the given numbers \(48.5\), \(39\), and \(32.5\) are the lengths of the sides of a triangle, we can determine the type of triangle (acute, right, or obtuse) by using the triangle inequality and the relationship of the squares of the sides.

1. **Triangle Inequality**: For three sides \(a\), \(b\), and \(c\):
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)

2. **Classifying the Triangle**:
- Calculate \(a^2 + b^2\) and compare it with \(c^2\):
- If \(a^2 + b^2 > c^2\), the triangle is acute.
- If \(a^2 + b^2 = c^2\), the triangle is right.
- If \(a^2 + b^2 < c^2\), the triangle is obtuse.

Let's label the sides as follows:
- \(a = 48.5\)
- \(b = 39\)
- \(c = 32.5\)

Now, without loss of generality, we'll assume \(c\) is the longest side. We will check the conditions mentioned above.

### Step 1: Check Triangle Inequality

- \(48.5 + 39 > 32.5 \quad (87.5 > 32.5) \quad \text{True}\)
- \(48.5 + 32.5 > 39 \quad (81 > 39) \quad \text{True}\)
- \(39 + 32.5 > 48.5 \quad (71.5 > 48.5) \quad \text{True}\)

All conditions are satisfied, so these lengths can form a triangle.

### Step 2: Check for the type of triangle

Now, we calculate \(a^2\), \(b^2\), and \(c^2\).

- \(a^2 = (48.5)^2 = 2352.25\)
- \(b^2 = (39)^2 = 1521\)
- \(c^2 = (32.5)^2 = 1056.25\)

Next, we calculate \(a^2 + b^2\):

\[
a^2 + b^2 = 2352.25 + 1521 = 3873.25
\]

Now, compare this with \(c^2\):

- \(a^2 + b^2 = 3873.25\)
- \(c^2 = 1056.25\)

Since \(a^2 + b^2 > c^2\), we conclude that the triangle is **acute**.

Thus, the triangle with sides \(48.5\), \(39\), and \(32.5\) is classified as an **acute triangle**.