In the ABC triangle, the angle is A = B = 75 degrees. Find BC if the area of the triangle is 36 cm.

univerkov | May 10, 2021 | education

So A = B is an isosceles triangle, then its height is:

h = 2 * S / BC = 72 / BC.

On the other hand:

h = 1 / 2BC * ctg (75 °).

Then:

BC ^ 2 = 144 / ctg (75 °) = 144 / (ctg (45 ° + 30 °)) = 144 * ctg (30) * ctg (45) / (ctg (30) * ctg (45) – 1) = 144 * √3 / (√3 – 1).

BC = 12 * √ (1 / (1 – 1 / √3)).

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.