In a right-angled triangle ABC, hypotenuse AB = 13 cm, legs AC = 12 cm, BC = 5 cm.

In a right-angled triangle ABC, hypotenuse AB = 13 cm, legs AC = 12 cm, BC = 5 cm. Find the sine, cosine and tangent of angle A.

ΔBAC – rectangular.

AB = 13 cm.

AC = 12 cm.

BC = 5 cm.

cos∠ВАС -?

sin∠ВАС -?

tg∠ВАС -?

According to the definition, the cosine of the angle ∠BAC is the ratio of the leg AC adjacent to this angle to the hypotenuse AB: cos∠BAC = AC / AB.

cos∠BAC = 12 cm / 13 cm = 0.923.

According to the definition, the sine of the angle ∠BAC is the ratio of the leg BC opposite to this angle to the hypotenuse AB: sin∠BAC = BC / AB.

sin∠BAC = 5 cm / 13 cm = 0.385.

The tangent of the angle ∠BAC is the ratio of the leg BC opposite to this angle to the adjacent leg AC: tg∠BAC = BC / AB.

tg∠BAC = 5 cm / 12 cm = 0.417.

tg∠ВАС = sin∠ВАС / cos∠ВАС.

tg∠BAC = 0.385 / 0.923 = 0.417.

Answer: cos∠BAC = 0.923, sin∠BAC = 0.385, tg∠BAC = 0.417.