In triangle ABC, angle C is 90 °, AB = 30 cm, AC = 3√19 cm. Find sin A.
| February 2, 2021 | education
First way.
By the Pythagorean theorem, we determine the length of the BC leg.
BC ^ 2 = AB ^ 2 – AC ^ 2 = 900 – 171 = 729.
BC = 27 cm.
Determine the sine of the angle BAC.
SinBAC = BC / AB = 27/30 = 9/10.
Second way.
Determine the cosine of the angle BAC.
CosBAC = AC / AB = 3 * √19 / 30 = √19 / 10.
Determine the sine of the angle BAC.
Sin2BAC + Cos2BAC = 1.
Sin2BAC = 1 – Cos2BAC = 1 – (19/100) = 81/100.
SinBAC = 9/10.
Answer: The sine of the ICA angle is 9/10.
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.
