In triangle ABC given: AB = BC = 10? AC = 2 √19, find sin A.
| April 2, 2021 | education
Consider a triangle ABC. Let’s draw the height BH.
Triangle ABC is isosceles because AB = BC.
Since triangle ABC is isosceles, the height BH is also the median, and therefore AH = HC = AC / 2 = 2 * √19 / 2 = √19.
Consider a right-angled triangle ABH. By the Pythagorean theorem:
AB ^ 2 = AH ^ 2 + BH ^ 2 = (√19) ^ 2 + BH ^ 2 = 10 ^ 2, BH ^ 2 = 100 – 19 = 81, BH = 9.
Then, since triangle ABH is rectangular, we get:
sin (A) = BH / AB = 9/10.
Answer: sin (A) = 9/10.
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