One of the acute angles of a right-angled triangle is 60 degrees and the sum of the small leg and

One of the acute angles of a right-angled triangle is 60 degrees and the sum of the small leg and the hypotenuse is 2.64 cm Find the length of the hypotenuse.

From the condition, we know that one of the acute angles of a right-angled triangle is 60 °, and the sum of the hypotenuse and the smaller leg is 2.64 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 opposite to 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 = 2.64;

3x = 2.64;

x = 0.88 cm leg of a right triangle.

We are looking for the hypotenuse 2x = 0.88 * 2 = 1.76 cm.