In triangle ABC the angle is C = 90º, BC = 10, sinB = 2 / √ (29). Find AC.

univerkov | April 30, 2021 | education

Knowing the sine of the angle ABC, we determine the cosine of this angle.

Sin2ABC + Cos2ABC = 1.

Cos2ABC = 1 – Sin2ABC = 1 – (2 / √29) ^ 2 = 1 = 1 – 4/29 = 25/29.

CosABC = 5 / √29

Determine the tangent of the angle ABC.

tgABC = SinABC / CosABC = (2 / √29) / (5 / √29) = 2/5.

Since the tangent of the angle is the ratio of the opposite leg to the adjacent leg, then:

tgABC = 2/5 = AC / BC = AC / 10.

AC = 10 * 2/5 = 4 cm.

Answer: The length of the AC segment is 4 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.