In triangle ABC, angle C is 90 degrees, BC = 12√6, AB = 30. Find the sine B
| May 25, 2021 | education
Since the angle C is 90 °, triangle ABC is right-angled with hypotenuse AB. Then, by the Pythagorean theorem, the leg AC is equal to:
√ (AB ^ 2 – BC ^ 2) = √ (30 ^ 2 – (12√6) ^ 2 = √36 = 6.
Using the definition of the sine of an angle, we get:
sin (B) = AC / AB = 6/30 = 1/5.
Answer: The sought sine of angle B is 1/5.
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