In triangle ABC, angle C is 90, AC is 15, cosine of angle B is √7 / 4. Find AB
| September 12, 2021 | education
Knowing the cosine of the angle ABC, we determine the sine of this angle.
Sin2ABC = 1 – Cos2ABC = 1 – (√7 / 4) 2 = 1 – 7/16 = 9/16.
SinABC = 3/4.
Through the sine of the angle and the opposite leg, we determine the length of the hypotenuse AB.
SinABS = AC / AB.
AB = AC / SinABC = 15 / (3/4) = 15 * 4/3 = 20 cm.
Answer: The length of the hypotenuse AB is 20 cm.
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