In triangle ABC, the angle C is 90 ° tgA = 3/4. find cosB.
| July 9, 2021 | education
Since tgA = 3/4, then BC refers to AC as 3: 4. Let’s denote BC 3x, and AC 4x.
By the Pythagorean theorem:
AB² = BC² + AC² = (3x) ² + (4x) ² = 9x² + 16x² = 25x².
AB = 5x.
Let us express the cosine B: cosB = BC / AB.
BC = 3x, AB = 5x, so cosB = 3x / 5x = 3/5 = 0.6.
Answer: cosB = 0.6.
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