One of the corners of a right-angled triangle = 60 degrees, and the sum of the hypotenuse

One of the corners of a right-angled triangle = 60 degrees, and the sum of the hypotenuse and the smaller leg = 50 cm. Find the hepotenuse.

Let triangle ABC be rectangular and angle B a straight line,

and the angle A = 60 °. Then the angle C = 180 ° – A – B = 180 ° – 60 ° – 90 ° = 30 °.

Then, opposite the smaller C angle, there is a smaller leg and its length:

| AB | = | AC | * sin (30 °) = 0.5 * | AC |.

Therefore, | AB | + | AC | = 1.5 * | AC |.

But by the problem statement, | AB | + | AC | = 50, which means:

1.5 * | AC | = 50, | AC | = 2 * 50/3 = 100/3.

Answer: the hypotenuse is equal to (100/3) cm.