In a triangle ABC, the angle C is 90 degrees, the sine of the outer angle at the vertex A is 7/25 AB = 5. Find the AC.
| July 19, 2021 | education
The sine of the outer corner of a triangle is equal to the sine of the inner corner adjacent to it.
SinBAC = SinBAД = 7/25.
Determine the cosine of the angle BAC from the basic trigonometric identity.
Sin2BAC + Cos2BAC = 1.
Cos2BAC = 1 – Sin2BAC = 1 – 49/625 = 576/625.
CosBAC = 24/25.
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 = 5 * 24/25 = 4.8 cm.
Answer: The length of the AC leg is 4.8 cm.
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