A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/2$ . If side C has a length of $4$ and the angle between sides B and C is $pi/12$ , what is the length of side A?

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Answer 1 · 2018-02-23T15:32:33

$A=1.04"cm"$

We have a triangle that looks like this:

enter image source here

Here, side B is the base leg, side C is the hypotenuse and side A is the vertical leg.

We can say the angle opposite to side A is $/_a$ , and the angle opposite to side C is $/_c$ .

$sina/A=sinb/B=sinc/C$

Since Side B doesn't matter here, we can say:

$sina/A=sinc/C$

We need to solve for $A$ . Simply rearrange:

$A=(Csina)/sinc$

Since $a=pi/12, C=4"cm"$ and $c=pi/2$ , we can input:

$A=(4*sin(pi/12))/sin(pi/2)$

$A=(4*0.259)/1$

$A=1.04"cm"$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2(pi)/2. If side C has a length of 4 4 and the angle between sides B and C is pi/12pi/12, what is the length of side A?