In a right-angled triangle ABC leg AC = 55, and the height CH, pubescent on the hypotenuse, is 44. Find the sin of angle ABC.
| May 23, 2021 | education
In a right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the leg AH.
AH ^ 2 = AC ^ 2 – CH ^ 2 = 3025 – 1936 = 1089.
AH = 33 cm.
According to the property of the CH height, drawn to the hypotenuse from the apex of the right angle, CH2 = AH * BH.
BH = CH ^ 2 / AH = 1936/33 = 176/3 cm.
AB = AH + BH = 33 + 176/3 = 275/3 cm.
Then SinABC = AC / AB = 55 / (275/3) = 3/5.
Answer: The sine of the angle ABC is 3/5.
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