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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