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

One of the corners of a right-angled triangle is 60 degrees, and the sum of the hypotenuse and the smaller leg is 60 cm. Find the hypotenuse of the triangle.

From the condition it is known that one of the angles of a right-angled triangle is 60 °, and the sum of the hypotenuse and the smaller leg is 60 cm. In order to find the hypotenuse of the triangle, we compose and solve a linear equation.

Let’s first of all find the degree measure of the third angle of the triangle:

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

Let us denote by the variable x the length of the smaller leg. The smaller leg lies opposite the smaller angle. The leg opposite to an angle of 30 ° is equal to half the hypotenuse.

Then the hypotenuse can be written as 2x.

2x + x = 60;

3x = 60;

x = 20 cm smaller leg,

then the hypotenuse of the triangle is 20 * 2 = 40 cm.