The acute angle of the triangle is 60 degrees. The sum of the hypotenuse and lesser leg = 2.64 cm.

The acute angle of the triangle is 60 degrees. The sum of the hypotenuse and lesser leg = 2.64 cm. What is the length of the hypotenuse?

First, we need to determine what the second acute angle of the right-angled triangle presented in the condition will be equal to, when it is known that the first is 60 °:

90 – 60 = 30.

As we know from the school curriculum, the leg that is opposite such an angle is smaller and is only half of the hypotenuse.

Then let it be expressed in terms of a.

Therefore, the hypotenuse will be equal to 2a.

Knowing that the sum of their lengths is 2.64 cm, we get:

2a + a = 2.64;

3a = 2.64;

a = 0.88;

0.88 * 2 = 1.76.

Answer: 1.76 cm.