A triangle with a radius of 10 cm is inscribed in a circle with one angle equal to 60 and the other 15.

A triangle with a radius of 10 cm is inscribed in a circle with one angle equal to 60 and the other 15. Find the area of the triangle?

Let’s find out what the third corner of this figure will be:

180 – (15 + 65) = 105.

Let’s find out what the first side will be equal to:

2 * 10 * sin60 ° = 20 sin60 °.

Let’s find out what the second side will be equal to:

2 * 10 * sin15 ° = 20 sin15 °.

Let’s find out what the third party will be equal to:

2 * 10 * sin105 ° = 20 sin105 °.

Let us find out what the area of this triangle will be equal to in this case:

Str = 20 sin60 ° * 20 sin15 ° * 20 sin60 ° / (4 * 10) = 200 * sin60 ° * sin15 ° * sin105 °;

sin60 ° = √3 / 2;

sin15 ° * sin105 ° = (√6 – √2) / 4 * (√6 + √2) / 4 = (6 – 2) / 16 = 1/4;

200 * 1/4 * √3 / 2 = 25√3.

Answer: 25√3.