The base of the pyramid is a right-angled triangle with a hypotenuse of 10 each side edge is 13.

The base of the pyramid is a right-angled triangle with a hypotenuse of 10 each side edge is 13. Find the height of the pyramid

Since the lengths of the side faces of the pyramid are equal, the vertex D of the pyramid is projected to the point H, the center of the triangle described near the triangle ABC.

Triangle ABC is rectangular, then the center of the circumscribed circle is the middle of the hypotenuse AB. AH = BH = AB / 2 = 10/2 = 5 cm.

DH is the height of the pyramid, perpendicular to AB, then in a right-angled triangle ADH, according to the Pythagorean theorem, DH ^ 2 = AD ^ 2 – AH ^ 2 = 169 – 25 = 144.

DН = 12 cm.

Answer: The height of the pyramid is 12 m.