In the rectangle ABCD, the diagonal AC = 3cm is drawn. It is known that the angle CAD = 37

univerkov | March 5, 2021 | education

In the rectangle ABCD, the diagonal AC = 3cm is drawn. It is known that the angle CAD = 37 degrees. Find S of rectangle ABCD.

In a right-angled triangle ACD, we define the lengths of the legs AD and CD.

CosCAD = AD / AC.

AD = AC * Cos370 = 3 * Cos370 ≈ 2.4 cm.

SinCAD = CD / AC.

CD = AC * Sin370 = 3 * Sin370 ≈ 1.8 cm.

Determine the area of the triangle ACD.

Sac = AD * CD / 2 = 2.4 * 1.8 / 2 = 2.16 cm2.

The AC diagonal divides the rectangle into two equal-sized right-angled triangles.

Then Savsd = 2 * Sasd = 2 * 2.16 = 4.32cm2.

Answer: The area of the rectangle ABCD is 4.32 cm2.

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