The bases of an isosceles trapezoid are 23 and cosine 27 of an acute angle of a trapezoid is 1/6, find the side.

The trapezium is isosceles. We find the length of the lateral side from a right-angled triangle, which is formed by drawing the height from the end of the smaller base to the larger one.

The heights form two equal right-angled triangles, respectively, their legs at acute angles of the trapezoid are equal:

x = (27 – 23) / 2 = 2;

Now we find the lateral side through the value of the cosine of the acute angle of the trapezoid:

cos A = x / y, where y is the side.

y = x / cos A = 2 / (1/6) = 12 cm.