One of the corners of a right-angled triangle is 60 degrees, and the difference between the hypotenuse

One of the corners of a right-angled triangle is 60 degrees, and the difference between the hypotenuse and the smallest leg is 15 cm. Find the hypotenuse.

Let us determine what the unknown acute angle will be equal to, when from the condition of the task we know that the known acute angle of our right-angled triangle is equal to 60 °:

90 – 60 = 30.

As you know, the side that lies opposite such an angle is half the size of the hypotenuse.

The same side is the smaller leg.

Let its length be equal to the variable a.

Then the length of the hypotenuse can be represented as 2a.

Since we know that their difference is 15 cm, then we write down the equation and find the hypotenuse:

2a – a = 15;

a = 15;

2 * 15 = 30.

Answer: 30 cm.