Question

classify each triangle as acute, right or obtuse.

10, 49.5, 50.5


these sides form a ____ triangle

Answer 1

u sure

Answer 2

To classify the triangle formed by sides of lengths 10, 49.5, and 50.5, we can first use the triangle inequality to determine if these lengths can form a triangle. The triangle inequality states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the inequalities:

1. \(10 + 49.5 > 50.5\)
- \(59.5 > 50.5\) (True)

2. \(10 + 50.5 > 49.5\)
- \(60.5 > 49.5\) (True)

3. \(49.5 + 50.5 > 10\)
- \(100 > 10\) (True)

Since all three conditions are satisfied, these sides do form a triangle.

Next, to determine if the triangle is acute, right, or obtuse, we can use the lengths to verify:

1. Find the square of each side:
- \(a = 10\) → \(a^2 = 100\)
- \(b = 49.5\) → \(b^2 = 2450.25\)
- \(c = 50.5\) → \(c^2 = 2550.25\)

2. Check the relationship between \(c^2\) and \(a^2 + b^2\):
- \(a^2 + b^2 = 100 + 2450.25 = 2550.25\)
- \(c^2 = 2550.25\)

Since \(c^2 = a^2 + b^2\), this means the triangle is a **right triangle**.

Thus, the sides 10, 49.5, and 50.5 form a **right triangle**.

Answer 3

Let's verify the calculations step by step to ensure accuracy.

Given sides: \(a = 10\), \(b = 49.5\), and \(c = 50.5\).

### Step 1: Check if these can form a triangle

Using the triangle inequality:

1. \(10 + 49.5 > 50.5\) → \(59.5 > 50.5\) (True)
2. \(10 + 50.5 > 49.5\) → \(60.5 > 49.5\) (True)
3. \(49.5 + 50.5 > 10\) → \(100 > 10\) (True)

All inequalities are satisfied, so these can form a triangle.

### Step 2: Determine the type of triangle

We will compare \(c^2\) (where \(c\) is the longest side) with \(a^2 + b^2\).

- **Calculate \(a^2\):**
\[
a^2 = 10^2 = 100
\]

- **Calculate \(b^2\):**
\[
b^2 = 49.5^2 = 2450.25
\]

- **Calculate \(c^2\):**
\[
c^2 = 50.5^2 = 2550.25
\]

### Step 3: Compare \(c^2\) with \(a^2 + b^2\)

- Calculate \(a^2 + b^2\):
\[
a^2 + b^2 = 100 + 2450.25 = 2550.25
\]

Now compare:
- \(c^2 = 2550.25\)
- \(a^2 + b^2 = 2550.25\)

Since \(c^2 = a^2 + b^2\), the triangle is classified as a **right triangle**.

### Conclusion

The analysis is correct; the sides 10, 49.5, and 50.5 do indeed form a **right triangle**. Thank you for prompting the re-check!