Knowing that the side length of a regular pentagon is 500, how do you find the radius of its circums

The diameter of the circumscribed circle is the diagonal of the square, and the diagonal length of the square is 500 times the root number 2

Then the radius of the circumscribed circle is 250 times the root number 2

The answer is: it needs to be represented by trigonometric functions.

Solution: Even od. oad=90+45=135°

Let the side length of the square be x, then oa = (2)x

5^2)=((√2)x)^2)+(x^2)-2•√(2)x•x•cos135°

25=5(x^2 )∴x=√(5)

The side length of the inscribed square is (5).

The area formula for a square is:

Area = side length, expressed in letters: s = a (s refers to the area of the square, a refers to the length of the side of the square).

A square is a special rectangle, a special rectangle, and the area of the rectangle = the area of the rectangle = the length and width.

In letters, it is: s=ab (s is the area of the rectangle, a is the length of the rectangle, and b is the width of the rectangle).

Positive five-sided hand base shape.

The central angle of each pair.

It is 360° 5 72°, half Bicha Jin diameter (45 2) sin (72° 2).

Centimeter. Celebration of chaos.

The relationship between the side length and the radius of a regular pentagon is: side length = radius.

So, the radius sought = 95 cm).

It can also be found by trigonometric relations: since the central angle of a pentagon is equal to 72 degrees, then its bright half angle is equal to 36 degrees.

If the center of the circle is made into a perpendicular line of one string (i.e., one side), then the perpendicular foot divides the string in two equal parts, and 95 2 = In the obtained right-angle Jingqing regular triangle: sin36°=

r=cm).

The relationship between the radius of the circumscribed circle and the length of the side of a regular pentagon is: the radius of the circle is half the length of the side.

The radius of the yen is half the length of the side.

Connecting the center of the circle with the five vertices gives you five isosceles triangles.

Take one of them as the object of study.

Let the radius be r and the side length of the pentagon be l

Apex angle = 360° 5 = 72°

According to the sinusoidal theorem.

l/sin36°=2r

The solution yields l=2sin36°r

Each inner base angle of a regular pentagon is (5 2) 180° 5 108°

Connecting the two ends of the center of the circle and one side gives an isosceles triangle with a base angle of 108° 2 54° and a top angle of 180° 2 54° and a 72° of Yunyinjin

Let the length of the side fight of the regular pentagonal be a, and the radius of the circumscribed circle is r, then r a (2cos54°) a (2sin36°).

The following is the method for finding sin36°:

Since sin36° sin(180° 36°) sin144° 2sin72°cos72°

4sin36°cos36°[2(cos36°)^2－1]

This gives 8(cos36°) 3 4cos36° 1 0

2cos36°＋1)[4(cos36°)^2－2cos36°－1]＝0

It is solved by 4(cos36°) 2 2cos36° 1 0.

cos36°＝(1＋√5)/4,sin36°＝√1－(cos36°)^2]＝√10－2√5)/4.

So r a (2sin36°) a [2 (10 2 5) 4] 2a (10 2 5).

(50＋10√5)a/10

It is found using the sinusoidal principle in trigonometric functions.

The sine value is equal to the opposite side of the right triangle than the hypotenuse. This hypotenuse is the radius of the circumscribed circle, and the opposite side is equal to 1 2The corresponding angle on each side of the regular pentagon is one-fifth of the circumferential shielding angle, i.e., 360 5 = 72

Then the formula for calculating the positive five trapped sides is:

sin36*r*10

Answer: I fainted and disturbed Chun, and I began to see that the positive side was slowing down. The circumference angle of each side of the positive 5-sided is a = 360 ° 5 = 72 ° and the top angle is 72 °, and the bottom edge is 150 in the waist triangle, and the waist length is a circumscribed circle and a semicircle r, so:

rsin(a2)=150 2(d2)sin36°=75 so:d=150 sin36°so:d=150

The corresponding central angle of each oak edge is 360°, and the trace beats Tanzitong 5=72°

Edge length = 2*r*sin(36°).