In a rectangular trapezoid ABCD (angle D = angle C = 90 *, AC and BD – bases) AB = 9,

In a rectangular trapezoid ABCD (angle D = angle C = 90 *, AC and BD – bases) AB = 9, BD = 12, AD = 15. Find the sine, cosine and tangent of the CBD angle.

In triangle ABD, the Pythagorean theorem holds, 82 + 122 = 152.

225 = 225.

Then triangle ABD is rectangular with right angle ABD.

The sought angle CBD = ADB as the intersecting angles at the intersection of parallel straight lines ВС and АD of the secant ВD.

Then CosСВD = CosАDВ = ВD / АD = 12/15 = 4/5.

SinSVD = SinADV = AB / AD = 9/15 = 3/5.

tgSVD = tgADB = AB / BD = 9/12 = 3/4.

Answer: CosСВD = 4/5, SinСВD = 3/5, tgСВD = 4/5.