Find the sine cosine and the tangent of the angles A and B of a triangle ABC with a right angle C if B and c is 8 and B is 17.

| August 2, 2021 | education

Δabc – rectangular.

bc = 8 cm.

ab = 17 cm.

∠c = 900.

sina -?

cosa -?

tga -?

sinb -?

cosb -?

tgb -?

The sine of angle ∠a is the ratio of the leg bc opposite to this angle to the hypotenuse ab: sina = bc / ab.

According to the definition, the cosine of the angle ∠a is the ratio of the leg ac adjacent to this angle to the hypotenuse ab: cosa = ac / ab.

The tangent of the angle ∠a is the ratio of the leg bc opposite to this angle to the adjacent leg ac: tga = bc / ab.

We find the leg ac of a right-angled triangle by the Pythagorean trademark: ac = √ (ab ^ 2 – cb ^ 2).

ac = √ ((17cm) ^ 2 – (8cm) ^ 2) = 15cm.

sina = 8cm / 17cm = 0.47.

cosa = 15 cm / 17 cm = 0.88.

tga = 8 cm / 15 cm = 0.53.

sinb = 15 cm / 17 cm = 0.88.

cosb = 8 cm / 17 cm = 0.47.

tgb = 15 cm / 8 cm = 1.87.

Answer: sina = 0.47, cosa = 0.88, tga = 0.53, sinb = 0.88, cosb = 0.47, tgb = 1.87.



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