In triangle ABC, angle C = 90 degrees, AB = 5, cos B = 3/5 find AC.
| April 26, 2021 | education
In a right-angled triangle, the cosine of an acute angle is equal to the ratio of the adjacent leg to the hypotenuse.
In triangle ABC: ∠ B – acute, BC – adjacent leg, AB – hypotenuse.
BC: AB = cos ∠ B.
BC: 5 = 3/5.
5 x BC = 5 x 3.
5 x BC = 15.
BC = 15: 5.
BC = 3.
By the Pythagorean theorem:
AC ^ 2 + BC ^ 2 = AB ^ 2.
AC ^ 2 = AB ^ 2 – BC ^ 2.
AC ^ 2 = 5 ^ 2 – 3 ^ 2.
AC ^ 2 = 25 – 9.
AC ^ 2 = 16.
AC = √16.
AC = 4 or -4.
Answer -4 does not work because the length of the side of a triangle cannot be expressed as a negative number.
Answer: the AC side is 4.
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