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

One of the corners of a right-angled triangle is 60 degrees, and the difference between the hypotenuse and the smaller boat is 4 cm, find all sides.

From the condition it is known that one of the angles of a right-angled triangle is 60 °, and the difference between the hypotenuse and the smaller leg is 4 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 = 4;

x = 4 cm smaller leg,

then the hypotenuse of the triangle is 2 * 4 = 8 cm.