Given a triangle ABC, AB = AC, AH-height, AH = 5.2 cm, AB = 10.4 cm, find the angles ABC.

Let us determine what the sine of angle B will equal, which is located in a right-angled triangle ABH, if from the condition of our problem we know for sure that the length of AB (hypotenuse) is 10.4 centimeters, and the length of AH is 5.2 centimeters:

sin B = 5.2: 10.4 = 1/2.

This corresponds to an angle of 30 °.

According to the condition of the task, in the original triangle AB = AC, that is, it is isosceles, then the angle C is also equal to 30 °.

Now we can determine the magnitude of the angle A:

180 – 2 * 30 = 120.

Answer: B = C = 30 °, A = 120 °.