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MATH / In the diagram below, we have AB=24 and ∠ADB=90^(∘). If sinA=(2)/(3) and sinC=(3)/(4), then what is BC? [asy] pair A,B,C,D; A = (0,0); B = (8*sqrt(5),16); D = (8*sqrt(5),0); C = (8…

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problem

In the diagram below, we have AB=24AB = 24 and ∠ADB=90∘\angle ADB =90^\circ. If sinA=23\sin A = \frac23 and sinC=34\sin C = \frac34, then what is BCBC? [asy] pair A,B,C,D; A = (0,0); B = (8*sqrt(5),16); D = (8*sqrt(5),0); C = (8*sqrt(5) + 5.3333*sqrt(7),0); draw(D--B--A--C--B); label("AA",A,SW); label("BB",B,N); label("CC",C,SE); label("DD",D,S); draw(rightanglemark(B,D,A,43)); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram below, we have AB=24 and ∠ADB=90^(∘).  If sinA=(2)/(3) and sinC=(3)/(4), then what is BC?


[asy]
pair A,B,C,D;
A = (0,0);
B = (8*sqrt(5),16);
D = (8*sqrt(5),0);
C = (8*sqrt(5) + 5.3333*sqrt(7),0);
draw(D--B--A--C--B);
label("A",A,SW);
label("B",B,N);
label("C",C,SE);
label("D",D,S);
draw(rightanglemark(B,D,A,43));
[/asy]
Original LaTeX notation
In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$.  If $\sin A = \frac23$ and $\sin C = \frac34$, then what is $BC$?


[asy]
pair A,B,C,D;
A = (0,0);
B = (8*sqrt(5),16);
D = (8*sqrt(5),0);
C = (8*sqrt(5) + 5.3333*sqrt(7),0);
draw(D--B--A--C--B);
label("$A$",A,SW);
label("$B$",B,N);
label("$C$",C,SE);
label("$D$",D,S);
draw(rightanglemark(B,D,A,43));
[/asy]

level

Level 1

type

Precalculus

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Source and history

task_id
5ab7a09e-9d7d-5dbe-b517-825cdb8ee237
task_key
precalculus--test--5ab7a09e-9d7d-5dbe-b517-825cdb8ee237
task_revision_id
1
config / split
precalculus / test

Official source

initial import