<PRE><B>Question 1064313</B>
Let M be the point on TP where the bisector of angle TSP intersects TP
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Since triangle TSP is isosceles, SM is the perpendicular bisector of TP
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By Pythagorean Theorem,
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6^2 + SM^2 = 10^2
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SM^2 = 10^2 - 6^2 = 100 - 36 = 64
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SM = 8 cm
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Area(A) of triangle TSP = (1/2) * 12 * 8 = 48 cm^2
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now we can use area 48 cm^2 to solve for the other two altitudes
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48 = (1/2) * 10 * h
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5h = 48 
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h = 9.6
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The three altitudes are 9.6 cm, 9.6 cm, 8 cm
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