The base of the isosceles triangle is 8 cm and the angle between the sides is 60 degrees. Find the area of the triangle.

1. A, B, C – the vertices of the triangle. ∠А = 60 °. ВН – height.

2. ∠АВН = 180 ° – ∠АНВ – ∠А = 180 ° – 90 ° – 60 ° = 30 °.

3. The height drawn to the base in a given triangle is also the median and

divides the base of the speaker into two equal segments.

AH = CH = 8/2 = 4 cm.

4. In accordance with the properties of a right-angled triangle, the leg AH, located

against an angle of 30 °, equal to 1 / 2AB.

Therefore, AB = 2 x 4 = 8 cm.

5. We calculate the length of the HV:

BH = √AB²-AH² = √64 – 16 = √48 = 4√3 cm.

6. Calculate the area (S) of the triangle ABC:

S = АС х ВН / 2 = 8 х 4√3 / 2 = 16√3 cm².

Answer: the area of ​​a given triangle is 16√3 cm².