In rectangle ABCD, sides AB and BC are 8 and 15 cm. Find the value of the trigonometric functions of the angle BAC.

univerkov | July 15, 2021 | education

The ABC triangle is rectangular, then tgBAC = BC / AB = 15/8 = 1 (7/8).

From the right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 8 ^ 2 + 16 ^ 2 = 64 + 225 = 289.

AC = 17 cm.

Then SinВАС = ВС / АС = 15/17.

CosBAC = AB / AC = 8/17.

ctgBAC = 1 / tgBAC = 1 / (15/8) = 8/15.

Answer: The trigonometric functions of the angle BAC are equal: tgBAC = 1 (7/8), ctgBAC = 8/15, SinBAC = 15/17, CosBAC = 8/15.

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