A triangle has one side equal to 1 m, and the angles adjacent to it are equal to 30 ° and 45 °. Find the other sides of this triangle.

The sum of the inner angles of the triangle is 180, then the angle ACB = 180 – BAC – ABC = 180 – 30 – 45 = 105.

To determine the lengths of the sides of a triangle, we use the theorem of sines.

AB / SinACB = BC / SinBAC.

1 / Sin105 = BC / Sin30.

Sin105 = Sin (60 + 45) = Sin60 * Cos45 + Cos60 * Sin45 = (√3 / 2) * (√2 / 2) + (1/2) * (√2 / 2) = (√6 + √2 ) / four.

BC = Sin30 / Sin105 = (1/2) / (√6 + √2) / 4 = 2 / (√6 + √2) ≈ 0.518m.

1 / Sin105 = AC / Sin45.

AC = Sin45 / Sin105 = (√2 / 2) / (√6 + √2) / 4 = 2 * √2 / (√6 + √2) ≈ 0.732 m.

Answer: BC = 0.518 m, AC = 0.732 m.