# 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 30 cm. Find the hypotenuse.**

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 30 cm. In order to find the hypotenuse of the triangle, we compose and solve a linear equation.

Let’s first 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 = 30;

3x = 30;

x = 10 cm smaller leg, then 10 * 2 = 20 cm hypotenuse of the triangle.