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Math Help - Right angle: you know all 3 angles and length a, not b or c?

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    Right angle: you know all 3 angles and length a, not b or c?

    Could someone help me with this? I have a right angle triangle, 90, 30 and 60 degrees. Say the length of A is 30 inches. What would B and C be? Any help would be appreciated. thank you, johnr.
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    A riddle wrapped in an enigma
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    Quote Originally Posted by john r View Post
    Could someone help me with this? I have a right angle triangle, 90, 30 and 60 degrees. Say the length of A is 30 inches. What would B and C be? Any help would be appreciated. thank you, johnr.
    A is not a length. A length is specified using two letters, either AB, BC, or AC.
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    OK, say I know the length of one side of the triangle, but need to find the length of the hypotenuse and the other side of the triangle. john r.
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    Quote Originally Posted by john r View Post
    OK, say I know the length of one side of the triangle, but need to find the length of the hypotenuse and the other side of the triangle. john r.
    If you know trigonometry this is easy. If you don't know trig then you have to memorize something. I'll assume you don't know the trig.

    You have a 30, 60, 90 triangle. We can construct the ratios of these sides. They are always:
    \frac{a}{c} = \frac{1}{2}

    \frac{b}{c} = \frac{\sqrt{3}}{2}

    Note carefully that we need to know which angle is opposite which side in order to finish this problem. Without knowing that side a is opposite the 30 or 60 degree angle, I cannot proceed further. (But you should be able to take it from here.)

    -Dan
    Attached Thumbnails Attached Thumbnails Right angle: you know all 3 angles and length a, not b or c?-triangle.jpg  
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    A riddle wrapped in an enigma
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    Quote Originally Posted by john r View Post
    OK, say I know the length of one side of the triangle, but need to find the length of the hypotenuse and the other side of the triangle. john r.
    Can't draw that fast Tops!

    Ok, let's recall a couple of rules about a 30-60-90 triangle. The hypotenuse is twice the length of the shortest side (the side opposite the 30 degree angle). The side opposite the 60 degree angle is the long side and it is equal to the short side times the sqare root of 3.

    Look at my diagram. If the short side is 30 in. That makes the hypotenuse 60 inches, and the other leg 30\sqrt3 in.
    Attached Thumbnails Attached Thumbnails Right angle: you know all 3 angles and length a, not b or c?-right-triangle.bmp  
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by masters View Post
    Ok, let's recall a couple of rules about a 30-60-90 triangle. The hypotenuse is twice the length of the shortest side (the side opposite the 30 degree angle). The side opposite the 60 degree angle is the long side and it is equal to the short side times the sqare root of 3.
    We know that a = c/2. So what is b? According to Pythagoras:
    b^2 = c^2 - a^2

    b^2 = c^2 - \frac{c^2}{4} = \frac{3c^2}{4}

    Thus
    b = \frac{\sqrt{3}}{2} \cdot c

    -Dan
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    thank you all very much. I haven't had much use for geometry since college. thanks. and so quick, thankk you. john r.
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    You're very welcome, John. Good luck. Glad we could help.
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    I was amazed how quickly I found this website and how quickly I received multiple answers. Thanks for helping a 36 year old figure out something I knew by heart 15-20 years ago. john r
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    sine 30d=.5

    Drop the perpendicular from the top of an equilateral triangle. The angle is bisected to 30d. By Pythagorean theorem, the perpendicular= .5*3^2. This 30-60-90 triangle is similar to yours. If the base is 30, then the hypotenuse is 60 and the third side is .5*3(^.5)*60=30*(3^.5)
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