SOLUTION: using triangle ABC, find the length of the altitude from C to AB. The right triangle has two legs given. the leg BC has the length 7 and the leg AC has the length 24. I've alre

Question 564960: using triangle ABC, find the length of the altitude from C to AB. The right triangle has two legs given. the leg BC has the length 7 and the leg AC has the length 24.
I've already tried using the Pythagorean theorem for this problem, it doesn't work. I need an explanation....
Answer by issacodegard(60) (Show Source): You can put this solution on YOUR website!
Hi, suppose the altitude is CM, where M is such a point on AB. Since triangle ABC is a right triangle, its area is equal to half the product of the lengths of the legs. Also, if we rotate the triangle so that AB is the base, then the altitude CM will be the height in length. So the area is AB*CM, but it is also equal to BC*AC. So CM=BC*AC/AB. Ok, but how do we find AB? We use the Pythagorean Theorem: AB^2=BC^2+AC^2, so AB=sqrt(7^2+24^2)=sqrt(49+576)=sqrt(625)=25. So, CM=7*24/25=168/25=6.72
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