In a rectangle, the diagonal is 12 cm and the angle between the diagonals is 30 °. Find the area of the rectangle.

univerkov | September 28, 2021 | education

S = AB * BC;

Tr-k ABO – isosceles; <BOA = 30 °, so <ABC = 1/2 (180 ° – 30 °) = 75 °;

AB = BC * cos <ABC; cos 75 ° = 0.26; AB = 12 * 0.26 = 3.12 (cm);

<BCA = 15 °; cos 15 ° = 0.97;

AC = BC cos <BCA = 12 * 0.97 = 11.64 (cm);

S = 0.97 * 11 64 = 11.29 (cm²).

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