In a rectangular trapezoid, the bases are 6 cm and 11 cm, the smaller side is 4 cm.
| August 3, 2021 | education
In a rectangular trapezoid, the bases are 6 cm and 11 cm, the smaller side is 4 cm.Find the sine cosine and tanges of the acute angle of the trapezoid
Let’s draw the height of the CH trapezoid. Quadrangle ABCH is a rectangle, since the trapezoid is rectangular, and CH is height. Then AH = BC = 6 cm, CH = AB = 4 cm.
The length of the segment DH = AD – AH = 11 – 6 = 5 cm.
From the right-angled triangle СDН we determine the length of the hypotenuse СD.
CD ^ 2 = CH ^ 2 + DH ^ 2 = 16 + 25 = 41.
СD = √41 cm.
Determine tg, Cos and Sin of the ADC angle.
tgD = CH / DH = 4/5.
CosD = DH / CD = 5 / √41.
SinD = CH / CD = 4 / √41.
Answer: tgD = 4/5, CosD = 5 / √41, SinD = 4 / √41.
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