How to find the sides of an isosceles triangle if the base is known – 45.5 mm and the angle at the base is 53 °?

First, we determine all the angles of the triangle, knowing that the angles at the base are equal to each other, that is, 53 °. Then the angle opposite the base, or the angle at the apex is equal to: 180 ° – 53 ° – 53 ° = 180 ° – 106 ° = 74 °.

To find the lateral equal sides (c) of an isosceles triangle, we use the theorem of sines without reducing the formula, but immediately substituting the known values.

45.5 (mm) / sin 74 ° = in / sin 53 °, whence the side

h = 45.5 (mm) * sin 53 ° / sin 74 ° = 45.5 (mm) * 0.799 / 0.961 = 37.83 (mm).

Answer: sides h = 37.83 mm.