In triangle ABC AB = BC = 8 AH-height CH = 2 (4-√7) find the sine of angle B.
| April 16, 2021 | education
Determine the length of the segment ВН.
ВН = ВС – СН = 8 – 2 * (4 – √7) = 8 – 8 + 2 * √7 = 2 * √7 cm.
Since AH is the height, then the triangle ABH is rectangular, then CosABH = BH / AB = 2 * √7 / 8 = √7 / 4.
Determine the sine of the angle AВН.
Sin2ABH = Sin2ABC = 1 – Cos2ABC = 1 – 7/16 = (16 – 7) / 16 = 9/16.
SinABC = 3/4.
Answer: The sine of the angle ABC is 3/4.
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