Question

Which of the following combinations of sides and/or angles cannot form a right-angled triangle?

• A. 17, 8, 15
• B. \(1, \sqrt{2}, 45°\)
• C. 42°, 48, 5
• D. None

Answer 1

The Correct Option is D

A right-angled triangle follows the Pythagorean theorem, which states: \[ a^2 + b^2 = c^2 \] where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Let's check each option:
1. \(17, 8, 15\): \( 17^2 = 289 \), \( 8^2 = 64 \), and \( 15^2 = 225 \), and \( 289 \neq 64 + 225 \).
This combination does not form a right-angled triangle.
2. \(1, \sqrt{2}, 45^\circ\): This satisfies the conditions for forming a right-angled triangle.
3. \(42^\circ, 48^\circ, 5\): This combination satisfies the angle sum property of a triangle and can form a right-angled triangle.
Therefore, the correct answer is (D) None. All combinations are valid for forming a right-angled triangle.

The correct option is (D) : None