Question

the triangle is dropdown.

Explanation:

⚡ Using what you learned: the pythagorean theorem and its converse

Step 1: Identify the side lengths

Identify the three side lengths of the triangle:

• \( a = 6 \)
• \( b = 10 \)
• \( c = 10\sqrt{2} \) (longest side, potential hypotenuse)

Step 2: Calculate the squares of the sides

Calculate the square of each side length:

• \( a^2 = 6^2 = 36 \)
• \( b^2 = 10^2 = 100 \)
• \( c^2 = (10\sqrt{2})^2 = 100 \cdot 2 = 200 \)

Step 3: Compare the sum of the squares

Compare \( a^2 + b^2 \) to \( c^2 \):

• \( a^2 + b^2 = 36 + 100 = 136 \)
• Since \( 136 < 200 \), we have \( a^2 + b^2 < c^2 \).

Because the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse.

Answer:

obtuse