find length(ab) of equal triangle inside a circle of certain diameter, dia.114 inches

Hello,

Most people call me MUDDy, And I am new to math help.

I need to know how to find the length of a line (ab) on a equilateral triangle inscribed in a 114 inch circle. Here is the practical application it will be used for. If I carve a 114 inch diameter prop with three blades, I need to measure between all three tips of the blades to make sure they are perfectly orientated before balancing the prop. so I need to know the value of (ab) derived from a certain diameter. Thanks, and many good things to you and yours. Helping me here will help a lot more people all over the world.

Thanks

MUDDy(Hi)

Re: find length(ab) of equal triangle inside a circle of certain diameter, dia.114 in

You could divide the equilateral triangle into three identical isosceles triangles. The triangles will have equal sides of 57 (your radius) and equal angles of 30. The large other angle is 120 and the other side is what you are looking for. At this point it seems like you have a simple trig problem. Can you proceed from here?

Re: find length(ab) of equal triangle inside a circle of certain diameter, dia.114 in

Thank you for the help. It has been years since i went to college, and i have all but forgotten the trig i took, except for right triangles. i actually use that for getting the guy wires set for raising towers. lol.

thanks,

MUDDy

Re: find length(ab) of equal triangle inside a circle of certain diameter, dia.114 in

If my calculations are correct, your answer is

$\displaystyle 57\sqrt{3} \approx 98.73\textup{ inches}$

Re: find length(ab) of equal triangle inside a circle of certain diameter, dia.114 in

Thanks Grillage,

I used graph paper to get close, and your answer checks. And exact is what i needed for the application at hand. I really appreciate the help. I will post a special thanks when I make the video on youtube. Many will be thankful.

Keep smiling and have a ball. Many good things to you and yours.

MUDDy :)

Re: find length(ab) of equal triangle inside a circle of certain diameter, dia.114 in

As **grillage** suggested, if you take two of the blades as the equal sides of a 120°-30°-30° isosceles triangle, then the other side *x* (the distance between the blade tips) can be found by bisecting the triangle into two 30°-60°-90° triangles, and using one of them as follows:

$\displaystyle \cos(30^{\circ})=\frac{\frac{x}{2}}{57}$

$\displaystyle 57\cdot\frac{\sqrt{3}}{2}=\frac{x}{2}$

$\displaystyle x=57\sqrt{3}$

Re: find length(ab) of equal triangle inside a circle of certain diameter, dia.114 in

Thanks MUDDy, looking forward for the youtube clip.

Re: find length(ab) of equal triangle inside a circle of certain diameter, dia.114 in

TO GRILLAGE AND MarkFL2, THESE WERE VERY FAST RESPONSES, AND I APPRECIATE THE HELP AS MANY OTHERS WILL. I NOW HAVE AN ICON ON THE DESKTOP OF THIS SITE. BLESS ALL AND KEEP UP THE GREAT WORK. BEFORE I CAME HERE, I SEARCHED ALL OVER, AND TRIED TO JOG MEMORIES OF THE OLD LESSONS FROM TSTI, AND IT SEEMED THAT ALL I FOUND WAS ANSWERS TO THE AREA OF THE TRIANGLE, AND ANGLES. BUT AS IT SEEMS, THERE ARE MORE PRACTICAL APPLICATIONS TO ALL OF THE LINES AND MEASURES. AND WITHOUT THE PRACTICAL APPLICATIONS EXPLAINED OF APPLIED MATHs, THE WORLD MAY NEVER KNOW WHAT THOSE NUMBERS MEAN. THANKS TO Y'ALL, THEY WILL.

MUDDy