# Triangle ABC is rectangular. Angle C = 90 degrees, and the sine of angle A = 4/5. AC = 9. Find AB.

June 26, 2021 | education

| cosA = AC: AB- according to the definition of the cosine of the angle.

Let us express AB.

AB = AC: cosA.

Find cosA.

Since the sum of the angles of the triangle is 180o, the angle C is a straight line, then the angle A <90o, which means that cosA> 0.

It is known that sin2A + cos2A = 1.

cos2A = 1 – sin2A = 1 – (4/5) ^ 2 = 1 – 16/25 = 9/25 = (3/5) ^ 2.

cosA = 3/5.

Substitute the found value of cosA into the expression and calculate the value of AB.

AB = AC: cosA = 9: (3/5) = 9 * 5: 3 = 15.

Answer: side AB is 15.

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