Question

Classify each triangle as acute, right, or obtuse
4.8, 28.6, 29

Answer 1

To classify the triangle with side lengths 4.8, 28.6, and 29, we first need to check if it satisfies the triangle inequality theorem:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

Let’s assign \( a = 4.8 \), \( b = 28.6 \), and \( c = 29 \).

1. \( 4.8 + 28.6 = 33.4 > 29 \) (True)
2. \( 4.8 + 29 = 33.8 > 28.6 \) (True)
3. \( 28.6 + 29 = 57.6 > 4.8 \) (True)

Since all inequalities are satisfied, these sides can form a triangle.

Next, to classify the triangle (acute, right, or obtuse) based on the angles, we will use the converse of the Pythagorean theorem. We will compare the square of the longest side (\( c = 29 \)) with the sum of the squares of the other two sides (\( a \) and \( b \)).

Calculate \( a^2 + b^2 \):
\[
(4.8)^2 + (28.6)^2 = 23.04 + 817.96 = 841
\]

Calculate \( c^2 \):
\[
(29)^2 = 841
\]

Now we compare \( a^2 + b^2 \) and \( c^2 \):
\[
a^2 + b^2 = 841 \quad \text{and} \quad c^2 = 841
\]

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

**Conclusion**: The triangle with sides 4.8, 28.6, and 29 is a **right triangle**.