In triangle ABC, the length of the side AB is 6 cm, the angle B = 95 degrees, the angle A
| August 8, 2021 | education
In triangle ABC, the length of the side AB is 6 cm, the angle B = 95 degrees, the angle A = 55 degrees. Calculate the lengths of the sides BC and AC
The sum of the interior angles of the triangle is 180, then the angle ACB = (180 – 95 – 55) = 30.
Let’s apply the sine theorem for a triangle.
AB / SinACB = AC / SinABC.
AC = AB * SinABC / SinACB = 6 * Sin95 / Sin30 = 12 * Sin95 = 11.95 cm.
AB / SinACB = AC / SinBAC.
ВC = AB * SinBАC / SinACB = 6 * Sin55 / Sin30 = 12 * Sin55 = 9.83 cm.
Answer: The length of the AC side is 11.95 cm, the length of the BC side = 9.83 cm.
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