Thu, 16 Apr 2026 15:45:53 +0000

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Verify whether it is a right triangle, and if so, find the measure of the largest angle in degrees.
This trio of measurements sparks curiosity in many, especially across the US, where geometry intersects everyday life—from architecture to GPS navigation, and even in recreational hobbies like model building. So, can this triangle truly be right-angled, and what does that mean for understanding fundamental shapes? **Is This Triangle a Right Triangle? A Mathematical Verification**
A triangle is defined as right-angled if one of its angles measures exactly 90 degrees, based on the Pythagorean theorem. For triangle sides a, b, c, where c is the longest side, the condition becomes:
a² + b² = c²
Here, the sides are 7, 24, and 25 cm. Since 25 is the longest, check:
7² = 49
24² = 576
25² = 625 Add 49 and 576:
49 + 576 = 625
The equation holds exactly—this confirms the triangle is right-angled at the angle opposite the 25 cm side. **The Largest Angle: Confirmed by Geometry—90 Degrees**
In any triangle, the largest angle lies opposite the longest side. Since 25 cm is the longest and the angle opposite it is 90 degrees, this is the largest angle. This result aligns with core principles used in education, construction, and design across the United States where precision in shape verification matters for safety, alignment, and accuracy.