Find Altitude, Given Sides

In triangle ABC, a = 7, b = 8, and c = 9. Find the altitude of the triangle to side c.


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h2 = 72x2 = 82 – (9 – x)2
72x2 = 82 – (92 – 18x + x2) → 72x2 = 82 – 92 + 18xx2
49 = 64 – 81 + 18x → 18x = 66 → x = 11/3.
h2 = 72 – (11/3)2 = 49 – 121/9 = (441 – 121)/9 = 320/9 = (64/9) ⋅ 5
h = 8√5 / 3

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