The radio of a triangle inside circle

[H.M. Murdock]

Homework Statement

Greetings I 'd really appreciate some help with this problem thanks a lot in advance.

Find the radio of an equilateral triangle if it is inside a circle, and if a side of the triangle has a length of 24.

Homework Equations

I had to use a right triangle of the form 60-30-90
The Radio is the hypotenuse, while one catete (on the base of the triangle) is 1/2 side, and the other catete is the apothem.

The Attempt at a Solution

-half the base equals 1/2 side


On the right triangle of the form 60-30-90,

-The hypotenuse "b" (The Radio) is 2 times the first catete a

-The first catete "a" (The Apothem) equals 1, and

-The second catete "c" (Half the Base) equals square root of 3.


If one side is 24, what is the process in order find the hypotenuse (The Radio) of the right triangle?

The answer of the book is 8 square root of 3.



Thanks a lot

 

[H.M. Murdock]

Im sorry, I meant "the radio of a circle which has an equilateral triangle inside"

 

[Mark44]

What kind of a radio is it--AM or FM?

 

[Mark44]

1. Draw a circle.
2. Draw an equilateral triangle inside the circle.
3. Draw a line from one of the triangle's angles through the center of the circle to the opposite side of the circle. This line bisects the angle it starts from and passes through the center of the circle. Since it passes through the center of the circle, it is a diameter of the circle.
4. Draw a line from one of the other angles of the equilateral triangle to the end of the diameter.

The two lines you drew determine three triangles, all of which are 30-60-90 degree right triangles. Given that the original equilateral triangle has sides of length 24, you should be able to find all of the sides of the other triangles. The answer I get agrees with the one you reported.

 

[Mark44]

BTW, where are you getting your terms? I looked for "catete" in one dictionary AND in a math dictionary and didn't find it, so I still don't know what one is. I found apothem, but I don't think I've ever heard anyone use it.