In an isosceles trapezoid, the smaller base is 4, the lateral side is 13, and the tangent of the acute angle is 2.4.

In an isosceles trapezoid, the smaller base is 4, the lateral side is 13, and the tangent of the acute angle is 2.4. Find the larger base of the trapezoid.

The height of the trapezoid, the projection of the side and the side form a right-angled triangle, we take the projection as x, then:

2.4 * x – height.

By the Pythagorean theorem, we get the equation:

(2,4x) ^ 2 + x ^ 2 = 13 ^ 2;

6.76x ^ 2 = 169;

x ^ 2 = 25;

x = 5.

Since the trapezoid is isosceles, the larger base is:

4 + 2 * 5 = 14.

Answer: The value of the larger base is 14.