One of the angle of a right-angled triangle is 60 degrees, and the sum of the hypotenuse

One of the angle of a right-angled triangle is 60 degrees, and the sum of the hypotenuse and the smaller leg is 42 cm find the hypotenuse and leg

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 42 cm.

Let’s first find the third corner of a right-angled 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 = 42;

3x = 42;

x = 14 cm leg of a right triangle.

We are looking for the hypotenuse 2x = 14 * 2 = 28 cm.