In triangle ABC, side BC = 8 cm, angle A = 30 °, and angle C = 45 °. Find: AB.
| March 16, 2021 | education
The first way.
In triangle ABC we apply the theorem of sines for triangles and determine the length of the side AB.
AB / SinACB = BC / SinBAC.
AB = BC * SinACB / SinBAC.
AB = 8 * (√2 / 2) / (1/2) = 8 * √2 cm.
Second way.
Let’s build the height of the HВ. The BCH triangle is rectangular and isosceles, BH = CH = 4 * √2 cm.
In the ABН triangle, the ВН leg lies opposite the angle of 300, then AB = 2 * ВН = 2 * 4 * √2 = 8 * √2 cm.
Answer: The length of the AB side is 8 * √2 cm.
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