In a triangle, there are two sides a = 10, b = 8 and the angle α = 30 degrees opposite to side b.
| July 15, 2021 | education
In a triangle, there are two sides a = 10, b = 8 and the angle α = 30 degrees opposite to side b. Find the other two corners and the third side.
To solve the problem, apply the theorem of sines for a triangle.
ВС / SinA = AC / SinB.
SinB = AC * SinA / BC.
SinB = 10 * (1/2) / 8 = 0.625.
Angle CBA = arcsin0.625 ≈ 390.
Determine the value of the angle ACB.
Angle ACB = 180 – 30 – 39 = 1110.
By the theorem of sines, we determine the length of the side AB.
AB / SinC = BC / SinA.
AB = BC * SinC / SinA = 8 * Sin111 / Sin30 = 8 * 0.93 / (1/2) = 14.88 cm.
Answer: Angle C is 1110, angle B is 390, side AB is 14.88 cm.
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