The bases of the isosceles trapezoid are 11 and 27. The sides are equal to 17. Find the tangent of the acute angle of the trapezoid.

We draw the height from the obtuse angle of the trapezoid (with a smaller base) to a larger base. We get a right-angled triangle, the hypotenuse of which is 17, and one of the legs is 8. Using the Pythagorean theorem, we find the length of the second leg:
b = √ (c ^ 2 – a ^ 2) = √ (17 ^ 2 – 8 ^ 2) = √ (225) = 15.
Then the tangent of the acute angle of the trapezoid (the ratio of the opposite leg of the triangle to the adjacent one) will be equal to
tgα = b / a = 15/8.