In an isosceles trapezoid, the bases are 10 and 34 cm, and the side is 13. Find the sine, cosine

In an isosceles trapezoid, the bases are 10 and 34 cm, and the side is 13. Find the sine, cosine and tangent of the acute angle of the trapezoid.

1. Introduce the designation of the tops of the trapezoid by the symbols A, B, C, D. AB = 13 cm, Smaller base

BC = 10 cm.Larger base AD = 34 cm.

2. From the top B we draw the height BH to the base AD.

3. The length of the segment AH of the larger base of the trapezoid is calculated by the formula:

AH = (AD – BC) / 2.

AH = (34 – 10): 2 = 12 cm.

4. We calculate the length of the HВ height:

BH = √AB ^ 2 – AH ^ 2 = √13 ^ 2 – 12 ^ 2 = √169 – 144 = √25 = 5 cm.

5. Sine of the angle ВAD = ВН / AB = 5/13.

The cosine of the angle ВAD = 12/13.

The tangent of the angle ВAD = ВН / AН = 5/12.