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In triangle ABC, tan A = 3/4, tan B = 1, and a = 10. Find b in simplest radical terms?

The lowercase letters stand for the side opposite of the angle with the same uppercase letter. I can find the answer in decimal form, but I cannot solve it in radical terms.

Update:

Also, can you show your work as to how you got to that answer?

Update 2:

I got the answer to be (25 root 2) / 3, but I'm not sure how to get there. Can someone show me the work?

1 Answer

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  • Anonymous
    1 decade ago
    Favorite Answer

    Since tan(B) = 1, then B has to be 45 degrees. That's the only value of B less than 180 degrees that works.

    Using the identity tan^2(x) + 1 = sec^2(x), you can find sec(A) from tan(A). The reciprocal of this will be cos(A). You can then derive sin(A) from this using the identity sin^2(x) + cos^2(x) = 1.

    Now that you know B, sin(A), and a, you can find b by using the Law of Sines:

    sin(A)/a = sin(B)/b

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