In triangle ABC, angle C = 90, sinA = 13/14, AC = 6√3. Find AB.
March 15, 2021 | education
| Given: right-angled triangle ABC;
angle C = 90;
sin A = 13/14;
AC = 6√3;
Find: AB -?
Decision:
1) Let’s use the formula
cos ^ 2A + sin ^ 2A = 1;
cos ^ 2A = 1 – sin ^ 2A;
cos ^ 2A = 1 – 169/196;
cos ^ 2A = 196/25 – 169/25;
cos ^ 2A = 27/25;
cos A = 3√3 / 5;
2) Consider a right-angled triangle ABC. The cosine of the angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. Consequently:
cos A = AC / AB;
AB = CA / cos A;
AB = 6√3: 3√3 / 5;
AB = 6√3 * 5/3√3;
AB = 10.
Answer: AB = 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.