In a rectangular trapezoid, the acute angle is 60 degrees. The large side and the larger base are 4 cm

In a rectangular trapezoid, the acute angle is 60 degrees. The large side and the larger base are 4 cm each. Find a smaller base.

A rectangular trapezoid is called, in which one side is perpendicular to the base.

ВН- the height of the trapezoid;

AB – large lateral side;

AD – larger base;

∠А – acute angle of the trapezoid.

The segment of the larger base of the trapezoid, located between its heights, is equal to the length of the smaller base:

BC = HD.

In this way:

ВС = НD = АD – АН.

In order to calculate the length of the smaller base, we find the segment AH. For this, consider the triangle ΔАВН. Let’s use the cosine theorem.

The cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:

cos A = AH / AB;

AH = AB ∙ cos A;

AH = 4 ∙ 1/2 = 4/2 = 2 cm.

ВС = НD = 4 – 2 = 2 cm.

Answer: the length of the smaller base of the trapezoid is 2 cm.