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# Right-Triangle Trigonometry

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In the diagram below, we have $AB = 24$, $\angle ADB =90^\circ$, and angles $A$ and $C$ are acute. If $\sin A = \frac23$ and $\sin C = \frac34$, then what is $BC$?

Jul 5, 2018

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If Sin(A) = 2/3, then:

2/3 =BD / 24

BD =16

If sin(C) = 3/4, then:

3/4 = 16 / BC

BC =64 / 3 =21 1/3

Jul 5, 2018