# Find the area of a triangle if the base is 2, the angles at the base are 30 and 45.

December 29, 2020 | education

| Let’s designate a triangle: ABC.

Angle B = 180 ° – (30 ° + 45 °) = 105 °.

Let’s define BC and AB.

AC / Sin B = BC / Sin A;

BC = AC * Sin A / Sin B;

BC = 2 * 0.7071 / 0.9659;

BC = 1.47 cm.

AC / Sin B = AB / Sin C;

AB = AC * Sin C / Sin B;

AB = 2 * 0.5 / 0.9659;

AB = 1.04 cm.

Let’s omit the height BO. Consider a triangle ABO.

Angle ABO = 180 ° – (90 ° + 45 °) = 45 °. Angle ABO = Angle BAO – isosceles triangle.

AB = AO = 1.04 cm.

Let’s define the area.

S = AC * BO / 2 = 2 * 1.04: 2 = 1.04 cm2.

Answer: the area of the triangle is 1.04 cm2.

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.