SOLUTION: The side of the triangle are 20m, 25m , and 30m repectively. Find the Length of the altitude to the longest side?

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Question 868331: The side of the triangle are 20m, 25m , and 30m repectively. Find the Length of the altitude to the longest side?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Use Law of Cosines...

A picture will help but is not here included.

Pick the interior angle at the vertex of the 20 m and 30 m sides. Call the angle measure, t.
20%5E2%2B30%5E2-2%2A20%2A30%2Acos%28t%29=25%5E2
.
1300-625=1200cos%28t%29
cos%28t%29=675%2F1200
cos%28t%29=9%2F16
-
What is this value of t?
arcos%289%2F16%29=55.7711 degrees for more accuracy than needed.

Use the 20 meter length side as the hypotenuse of a right triangle which contains the altitude and part of the base side; we do not need the base side nor part of it here. We only want to compute the altitude. This altitude is:
highlight%28highlight%2820%2Asin%2855.7711%29%29%29.
16.5 meters.