In a triangle, the larger base angle is 45 degrees, and the height divides the base into 20

In a triangle, the larger base angle is 45 degrees, and the height divides the base into 20 cm and 21 cm lengths. Find the larger side

Since one of the angles of the triangle is 45, the right-angled triangle ABN, formed by the height BH is isosceles, AH = BH = 20 cm.

In a right-angled triangle BCH, we apply the Pythagorean theorem and determine the length of the hypotenuse BC.

BC ^ 2 = BH ^ 2 + CH ^ 2 = 20 ^ 2 + 21 ^ 2 = 400 + 441 = 841.

BC = 29 cm.

Answer: The length of the larger side of the triangle is 29 cm.