SOLUTION: In triangle ABC, tanA= 3/4, tanB= 1, and a=10; find b in simplest radical form. At the end, I got b= (10sin(45))/sin(36.9). How would I put this final answer 11.8 into radical

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Question 1194161: In triangle ABC, tanA= 3/4, tanB= 1, and a=10; find b in simplest radical form.
At the end, I got b= (10sin(45))/sin(36.9). How would I put this final answer 11.8 into radical form?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
In triangle ABC, tanA= 3/4, tanB= 1, and a=10; find b in simplest radical form.
At the end, I got b= (10sin(45))/sin(36.9). How would I put this final answer 11.8 into radical form?
~~~~~~~~~~~~~~~~~ 

Having  tan(A) = y/x = 3/4, you may think that y= 3, x= 4  and therefore  

    sin(A) =  =  = 3/5.


Next, having  tan(B) = 1, you conclude that  B = 45 degrees;  hence, sin(B) = .


After that, apply the sine law in the form

     = .


Everything except "b" is just known to you, so you write

    b =  = and substitute what you just know =  =  =  = 11.785 (approximately).


ANSWER.  b =  = 11.785 (approximately).

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The fact that the problem asks for the answer in simplest radical form tells you you can't use a calculator to get an APPROXIMATE degree measure for angle A and try to work from there.

Your answer is numerically approximately correct; and you obviously got that result using the law of sines, so I think you know what you are doing. So I won't solve the problem for you, but rather point you in the right direction.

To get the exact answer in simplest radical form, note that tan(A)=3/4 means sin(A)=3/5 and cos(A)=4/5.

Now use the law of sines....
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