In triangle ABC, angle C = 900. AC = 15cm, BC = 8cm. Find sine A, cosine A, tangent A, sine B, cosine B, tangent B.
| March 13, 2021 | education
Knowing the lengths of the legs of a right-angled triangle ABC, we determine the tangents of the angles BAC and ABC.
tgBAC = BC / AC = 8/15.
tgABC = AC / BC = 15/8 = 1 (7/8).
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 225 + 64 = 289.
AB = 17 cm.
Then SinBAC = BC / AB = 8/17.
CosBAC = AC / AB = 15/17.
In a right-angled triangle, the sine of one acute angle is equal to the cosine of the other, then:
SinABC = CosBAC = 15/17.
CosABC = SinBAC = 8/17.
Answer: SinBAC = 8/17, CosBAC = 15/17, tgBAC = 8/15.
SinABC = 15/17, CosABC = 8/17, tgABC = 1 (7/8).
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
