In triangle ABC, angle C is 90 degrees, the sine of angle A is 12/13. What is the AC leg if the hypotenuse is 13 cm.
| June 10, 2021 | education
From the basic trigonometric identity, we determine the cosine of the angle BAC.
Sin2BAC + Cos2BAC = 1.
Cos2BAC = 1 – Sin2BAC = 1 – 144/169 = 25/169.
CosBAC = 5/13.
In a right-angled triangle, the cosine of its acute angle is the ratio of the length of the adjacent leg to the length of the hypotenuse.
CosBAC = AC / AB.
AC = AB * CosBAC = 13 * 5/13 = 5 cm.
Answer: The length of the AC leg is 5 cm.
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.
