Question - Calculating the Length of the Hypotenuse in a Right-Angled Triangle
Solution:
The image shows a right-angled triangle with one side measuring 13 cm, which is the height, and the base measuring 23 cm. To solve for the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.Let's denote the hypotenuse as "c". The formula of the Pythagorean theorem is:a² + b² = c²Where:- a = one leg of the triangle (13 cm)- b = the other leg of the triangle (23 cm)- c = the length of the hypotenuse (what we need to find out)So we have:(13 cm)² + (23 cm)² = c²169 cm² + 529 cm² = c²698 cm² = c²Now, take the square root of both sides to find the length of the hypotenuse:c = √698 cm²c ≈ √700 cm²c ≈ 26.46 cmTherefore, the length of the hypotenuse is approximately 26.46 cm.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com