In a triangle ABC AC = BC, AB = 2, sine A = √15 / 4. Find AC.
| May 31, 2021 | education
Let’s draw from the vertex C of the triangle ABC the height, which is also the median, since by condition, AC = BC, then AD = BD = AB / 2 = 2/2 = 1 cm.
CD ^ 2 = AC ^ 2 – AD ^ 2 = AC ^ 2 – 1.
CD = AC * SinA.
CD ^ 2 = AC ^ 2 * Sin2A = 15 * AC ^ 2/16.
AC ^ 2 – 1 = 15 * AC ^ 2/16.
16 * AC ^ 2 – 16 = 15 * AC ^ 2.
AC ^ 2 = 16.
AC = 4 cm.
Answer: AC = 4 cm.
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