Diagonals of pentagon

Calculate the diagonal length of the regular pentagon:
a) inscribed in a circle of radius 12dm;
b) a circumscribed circle with a radius of 12dm.

Correct result:

u1 =  22.8254 dm
u2 =  28.2137 dm

Solution:

r1=12 cm A=360/(2 5)=36  sinA=a1/2:r1  a1=2 r1 sinA=2 r1 sin36 =2 12 sin36 =2 12 0.587785=14.10685 cm  u1=a1/2 (1+5)=14.1068/2 (1+5)=22.8254 dm
r2=12 cm  tanA=a2/2:r2  a2=2 r2 tanA=2 r2 tan36 =2 12 tan36 =2 12 0.726543=17.43702 cm  u2=a2/2 (1+5)=17.437/2 (1+5)=28.2137 dm



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
See also our right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Ten persons
    TUCWGKGHCVGBPEMEP75TVAR5LA Ten persons, each person makes a hand to each person. How many hands were given?
  • Each with each
    tenis_3 Five pupils from 3A class played table tennis. How many matches did they play with each other?
  • MO Z8–I–6 2018
    lich_1 In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
  • Diagonals
    diagonals_1 What x-gon has 54 diagonals?
  • Hexagon rotation
    hexagnos A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
  • Diagonals in diamond
    diagonalsf In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
  • Polygon 42
    12gon Which polygon has 42 more diagonals than sides?
  • Diagonals
    diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
  • N-gon
    ngon How many diagonals has convex 11-gon?
  • Regular hexagonal prism
    hexagon_prism2 Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
  • Hexagon ABCDEF
    hexagon_2 In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
  • Quadrilateral pyramid
    ihlan_rez In a regular quadrilateral pyramid, the side edge is e = 7 dm and the diagonal of the base is 50 cm. Calculate the pyramid shell area.
  • Coordinates of the intersection of the diagonals
    rectangle_inside_circle_1 In the rectangular coordinate system, a rectangle ABCD is drawn. The vertices of the rectangle are determined by these coordinates A = (2.2) B = (8.2) C = (8.6) D = (2.6) Find the coordinates of the intersection of the diagonals of the ABCD rectangle
  • Find the
    12gon Find the content of a regular 12 sided polygon, if its side a = 12 cm.
  • Pentadecagon
    220px-Regular_polygon_15_annotated.svg Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
  • Dodecagon
    clocks Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
  • Diamond area from diagonals
    kosostvorec In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?