In triangle ABC, the angle C is 90 degrees, the sine of A is 0.8, and AC is 9. Find AB.
| March 19, 2021 | education
1. Since the sine of angle A is the quotient of dividing the leg AB by the hypotenuse AB, we compose the ratio:
BC / AB = 0.8. Therefore, BC = 0.8AB units of measurement.
2. We calculate the length of the hypotenuse AB using the formula of the Pythagorean theorem:
AC² + BC² + AB².
AB² – BC² = 9² = 81.
AB² – (0.8AB) ² = 81.
AB² – 0.64AB² = 81.
0.36AB² = 81.
AB² = 225.
AB = √225 = 15 units.
Answer: AB = 15 units.
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