SOLUTION: In triangle ABC, length AB = 32, length BC = 10, and length AC = 26. If line segment CH is the altitude to segment AB and segment CM us the median to AB. What is the length of line
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-> SOLUTION: In triangle ABC, length AB = 32, length BC = 10, and length AC = 26. If line segment CH is the altitude to segment AB and segment CM us the median to AB. What is the length of line
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Question 1177732: In triangle ABC, length AB = 32, length BC = 10, and length AC = 26. If line segment CH is the altitude to segment AB and segment CM us the median to AB. What is the length of line segment HM? Found 2 solutions by math_helper, greenestamps:Answer by math_helper(2461) (Show Source):
We are given: a=10, b=26, c=32
Using the above figure as reference, we can use the Law of Cosines to find cos(A), which is the key to solving:
cos(A) = =
( we don't need to take arccos() here, as we are going to use cos(A) )
|AH| = 26*cos(A) = 26*(1600/1664) = 25
We know |AM| = (1/2)(32) = 16
|HM| = 25-16 = units
