Asked by Bri
So I’m given a triangle. The side lengths are 17, 18, and 19 is the hypotenuse. I have to find the height (x) algebraically.
How?
How?
Answers
Answered by
oobleck
There is no hypotenuse, since those sides do not form a right triangle.
Still, we can get the height. If we call those sides a,b,c then using the law of cosines,
17^2 = 18^2 + 19^2 - 2*18*19*cosA
cosA = 11/19
So, the height h (from C to AB), is given by
h/18 = sinA
h = 18 sinA = 18√(1 - (11/19)^2) = 72/19 √15
If you wanted the height to some other side, you'll have to go through these steps with the appropriate modifications.
Still, we can get the height. If we call those sides a,b,c then using the law of cosines,
17^2 = 18^2 + 19^2 - 2*18*19*cosA
cosA = 11/19
So, the height h (from C to AB), is given by
h/18 = sinA
h = 18 sinA = 18√(1 - (11/19)^2) = 72/19 √15
If you wanted the height to some other side, you'll have to go through these steps with the appropriate modifications.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.