In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectiv

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Question: In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?

Options:

Correct Answer: Right

Solution:

Since 8² + 15² = 17², triangle ABC is a right triangle.

In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?

In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?

Correct Answer: Right triangle

Step 1: Identify the lengths of the sides of triangle ABC. Here, side a = 8, side b = 15, and side c = 17.
Step 2: Use the Pythagorean theorem to check if the triangle is a right triangle. The theorem states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Identify the longest side. In this case, side c (17) is the longest side.
Step 4: Calculate the squares of the sides: a² = 8² = 64, b² = 15² = 225, and c² = 17² = 289.
Step 5: Add the squares of sides a and b: 64 + 225 = 289.
Step 6: Compare the sum with the square of side c: 289 (which is a² + b²) equals 289 (which is c²).
Step 7: Since the equation holds true (8² + 15² = 17²), conclude that triangle ABC is a right triangle.

Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
Triangle Classification – Triangles can be classified based on their side lengths and angles, including right, acute, and obtuse triangles.