Given the side BC = 3.5 cm, and two angles of the triangle ABC, angle B = 30 degrees

Given the side BC = 3.5 cm, and two angles of the triangle ABC, angle B = 30 degrees, angle C = 45 degrees. Find the third corner and the other two sides.

Since we know two angles by the setting condition, we can find the third angle by the property of the angles of the triangle;

Let’s write the formula for the sum of angles in a triangle;

180 ° = A + B + C, where A, B and C are the angles of the triangle;

Let’s substitute the data;

180 = A + 30 ° + 45 °;

Where;

A = 180 – (30 + 45) = 105 °;

Knowing the three angles and the side in the triangle, we use the sine theorem to find the remaining sides;

AB / sinC = BC / sinA = AC / sinB;

AC = BC * sinB / sinA = 3.5 * sin30 / sin105 = 1.75 / 0.9659 = 1.812cm;

AB = BC * sinC / sinA = 3.5 * √2 / 2 / 1/2 = 3.5 * √2 = 4.9cm.