One of the acute angles of a right-angled triangle is 60 degrees and the difference between the hypotenuse

One of the acute angles of a right-angled triangle is 60 degrees and the difference between the hypotenuse and the smaller leg is 15 cm, find the hypotenuse and the smaller leg.

From the condition, we know that one of the acute angles of a right-angled triangle is 60 °, and the difference between the hypotenuse and the smaller leg is 15 cm.

Let’s first find the third corner of a right triangle, knowing that the sum of the angles of the triangle is 180 °.

180 ° – 90 ° – 60 ° = 30 ° third corner of the triangle.

It is known that a leg lying opposite an angle of 30 ° is equal to half of the hypotenuse, and it is also known that a hundred opposite the smaller angle of a right-angled triangle lies the smaller side.

Let’s compose and solve the equation.

Let the smallest leg be x and the hypotenuse be 2x.

Based on the condition:

2x – x = 15;

x = 15 cm leg of a right-angled triangle.

We are looking for the hypotenuse 2x = 15 * 2 = 30 cm.