In triangle ABC, angle C = 90 sin a 8/9 AC = 2 √17 find AB.
| April 11, 2021 | education
Using the basic trigonometric identity, we find cos (a):
cos (a) = √ (1 – sin ^ 2 (a)) = √ (1 – (8/9) ^ 2 = √17 / 81.
Then:
tg (a) = sin (a) / cos (a) = 8/9 * 9 / √17 = 8 / √17.
The hypotenuse AB of a right triangle is equal to:
AB = AC * tg (a) = 2 * √17 * 8 / √17 = 16.
Answer: the required side AB is 16.
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