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# Points $A$, $B$, $C$, and $T$ are in space such that each of $\overline{TA}$, $\overline{TB}$, and $\overline{TC}$ is perpendicular to the o

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Points $A$, $B$, $C$, and $T$ are in space such that each of $\overline{TA}$, $\overline{TB}$, and $\overline{TC}$ is perpendicular to the other two. If $TA = TB = 10$ and $TC = 9$, then what is the volume of pyramid $TABC$?

michaelcai  Oct 12, 2017

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Let the base of TABC be triangle BCT.

TB and TC are perpendicular, so we can let TB and TC be the base and height of the triangle.

area of BCT  =  (1/2)(10)(9)

area of BCT  =  45

TA is perpendicular to the base, so its length = the height of TABC

volume of TABC  =  (1/3)(area of base)(height)

volume of TABC  =  (1/3)(45)(10)

volume of TABC  =  150  cubic units

hectictar  Oct 12, 2017
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#1
+6959
+2

Let the base of TABC be triangle BCT.

TB and TC are perpendicular, so we can let TB and TC be the base and height of the triangle.

area of BCT  =  (1/2)(10)(9)

area of BCT  =  45

TA is perpendicular to the base, so its length = the height of TABC

volume of TABC  =  (1/3)(area of base)(height)

volume of TABC  =  (1/3)(45)(10)

volume of TABC  =  150  cubic units

hectictar  Oct 12, 2017

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