Find the sine, cosine and tangent of the acute angle of an isosceles trapezoid

Find the sine, cosine and tangent of the acute angle of an isosceles trapezoid, the base difference of which is 8cm, and the sum of the sides is 10cm.

An isosceles trapezoid is a trapezoid in which the sides are equal.

Since the difference in the lengths of the two bases of the trapezoid is 8 cm, and the segments AH and KD have the same length, then:

AH = KD = (AD – BC) / 2;

AH = KD = 8/2 = 4 cm.

Since the sum of the lengths of the sides is 10 cm, then:

AB = CD = 10/2 = 5 cm.

Consider a triangle ABN formed by the height of the VN.

cos A = AH / AB;

cos A = 4/5 = 0.8.

To calculate the sine and tangent of angle A, you need to find the length of the BH. Let’s apply the Pythagorean theorem:

AB ^ 2 = BH ^ 2 + AH ^ 2;

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 5 ^ 2 – 4 ^ 2 = 25 – 16 = 9;

BH = √9 = 3 cm.

sin A = BH / AB;

sin A = 3/5 = 0.6;

tg A = BH / AH;

tg A = 3/4 = 0.75.

Answer: cos A = 0.8; sin A = 0.6; tg A = 0.75.