In an acute-angled triangle ABC, the height of AH is 20√3, and the side AB = 40. Find angle B.
| August 4, 2021 | education
In the AВН triangle we find the ВН leg. By the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 40 ^ 2 – (20√3) ^ 2 = 1600 – 400 * 3 = 1600 – 1200 = 400. BH = √400 = 20.
By definition, the cosine of an acute angle of a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. With respect to the triangle ABH we have: cos B = BH / AB = 20/40 = ½.
Answer: 1/2.
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