In triangle ABC, angle c is 90 degrees AB is 10 cosine B is 4/5 find AC.
| August 7, 2021 | education
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.
Then, in a right-angled triangle ABC:
CosABC = BC / AB.
BC = AB * CosABC = 10 * 4/5 = 8 cm.
By the cosine theorem, we determine the length of the leg AC.
AC ^ 2 = AB ^ 2 – BC ^ 2 = 100 – 64 = 36.
AC = 6 cm.
Answer: The length of the AC leg is 6 cm.
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