In the rectangle ABCD, AC = 6, angle ACB = 60 °. Find: 1) CA * CD, 2) AD * CA, 3) BC * DA.

univerkov | July 1, 2021 | education

In a right-angled triangle ACD <ACD = 60 °, <CAD = 90 ° – 60 ° = 30 °.

CD = 1/2 AC = 3; (leg lying opposite an angle of 30 °);

By the Pythagorean theorem:

AD² = AC² – CD² = 36 – 9 = 27;

AD = √27 = 3 √3;

CA * CD = 6 * 3 = 18;

AD * CA = 3 √3 * 6 = 18 √3;

BC * AD = AD² = 27.

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