# In triangle ABC, angle C = 90 degrees, sine A = 3/5, AC = 4. Find AB.

October 7, 2021 | education

| Let us express the sine of the angle A of a right-angled triangle: sinA = BC / AB = 3/5, that is, BC refers to AB as 3 to 5. Let BC = 3x, AB = 5x.

By the Pythagorean theorem: AB² = BC² + AC².

AC² = AB² – BC² = (5x) ² – (3x) ² = 25x² – 9x² = 16x².

AC = 4x.

Since AC = 4, we calculate the value of the variable x: 4x = 4; x = 1.

Hence, AB = 5x = 5 * 1 = 5.

Answer: AB length is 5.

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