Find the area of a rectangle, one side of which is 12 cm, and the cosine of the angle between the other side and the diagonal is 0.6.

univerkov | January 9, 2021 | education

Knowing the cosine of the AСD angle, we determine its sine.
Cos2AСD + Sin2AСD = 1.
(0.6) 2 + Sin2AСD = 1.
Sin2AСD = 1 – 0.36 = 0.64.
SinAСD = 0.8.
Determine the tangent of the angle of the AСD.
tgAСD = SinAСD / CosAСD = 0.8 / 0.6 = 4/3 = 1 (1/3) = AD / СD.
Let’s define the side of the СD.
СD = BP / tgAСD = 12 / (4/3) = 12 * 3/4 = 9 cm.
Determine the area of the rectangle.
S = AD * СD = 12 * 9 = 108 cm2.
Answer: The area of the rectangle is 108 cm2

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