The bases of an isosceles trapezoid are 7 and 15 the sides of the trapezoid are 8.

| July 25, 2021 | education

The bases of an isosceles trapezoid are 7 and 15 the sides of the trapezoid are 8. Find the cosine of the acute angle of the trapezoid.

Isosceles is a trapezoid in which the sides are equal.

In order to find an acute angle, we draw the heights of HV and CN.

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

AH = ND = (AD – BC) / 2;

AH = ND = (15 – 7) / 2 = 8/2 = 4 cm.

Consider the triangle ΔАВН. This triangle is rectangular with a right angle ∠C. To calculate the cosine of an acute angle, we apply 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;

cos A = 4/8 = 1/2.

Answer: the cosine of an acute angle of an isosceles trapezoid is 1/2, which corresponds to an angle of 60º.



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