# One of the corners of a right-angled triangle is 60 degrees and the distance between the hypotenuse

One of the corners of a right-angled triangle is 60 degrees and the distance between the hypotenuse and the smaller carriage is 15 cm. Find the length of the hypotenuse.

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 is the smaller leg and its length:

| AB | = | AC | * sin (30 °) = 0.5 * | AC | or | AC | = 2 * | AB |

Therefore, | AC | – | AB | = 2 * | AB | – | AB | = | AB |.

But by the problem statement, | AC | – | AB | = 15, which means:

| AB | = 15, | AC | = 2 * | AB | = 2 * 15 = 30.

Answer: The hypotenuse is 30 cm.

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