In a right-angled triangle ABC leg AC = 55 and the height CH lowered to the hypotenuse is 44.
| April 29, 2021 | education
In a right-angled triangle ABC leg AC = 55 and the height CH lowered to the hypotenuse is 44. Find the sin of the angle ABC.
Triangles АСН and ВСН are similar in acute angle, angle СНН = АСН.
CosACH = CH / AC = 44/55 = 4/5.
Then Sin2ACH = 1 – Cos2ACH = 1 – 16/25 = 9/25
SinACH = SinCBH = SinABC = 3/5.
Answer: The sine of the angle ABC is 3/5.
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