One of the corners of a right-angled triangle is 60 degrees and the sum of the hypotenuse and the smaller

One of the corners of a right-angled triangle is 60 degrees and the sum of the hypotenuse and the smaller of the leg is 26.4. find the hypotenuse of the triangle.

In a right-angled triangle, the acute angles add up to 90 degrees. This means that the second acute angle of our triangle is 90 ° – 60 ° = 30 °.

In any triangle, opposite the larger angle lies the larger side, opposite the smaller angle, the smaller side. This means that the larger leg lies opposite the 60 ° angle, and the smaller leg lies opposite the 30 ° angle.

Let’s denote the smaller leg a, the hypotenuse c. It is known that the sum of the smallest leg of the t hypotenuse is equal to (a + c) or 26.4.

In a right-angled triangle, the leg opposite to an angle of 30 ° is equal to half the hypotenuse, i.e. a = 0.5s.

Let’s combine the equations into a system and solve it.

a + c = 26.4; a = 0.5c – substitute the expression 0.5c in the first equation of the system instead of a;

0.5c + c = 26.4;

1.5c = 26.4;

c = 26.4: 1.5;

c = 17.6 – hypotenuse.

Answer. 17.6.