Question

If \( \triangle ABC \) has \( AB = 13 \) cm, \( BC = 12 \) cm, and \( AC = 5 \) cm, then \( \angle C \) is:

• A. \( 90^\circ \)
• B. \( 30^\circ \)
• C. \( 60^\circ \)
• D. \( 45^\circ \)

Hint:

A triangle is a right-angled triangle if it satisfies the Pythagorean theorem: [\ c^2 = a^2 + b^2. \]

Answer 1

The Correct Option is A

Using the Pythagorean theorem:
[\ AB^2 = AC^2 + BC^2. 13^2 = 5^2 + 12^2. \] 169 = 25 + 1 \[ 169 = 1 \] Since the equation holds, \( \triangle ABC \) is a right triangle with \( \angle C = 90^\circ \).