Cosine - examples

  1. Cylinder horizontally
    CylindricalSegment_1000 The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
  2. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  3. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  4. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 19 cm and 80 cm long and angle them clamped is 90°.
  5. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 11 cm.
  6. Forces
    ijk In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  7. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long.
  8. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  9. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles.
  10. Pentagon
    5gon Calculate the area of regular pentagon, which diagonal is u=14.
  11. Cone
    cone-blue Calculate volume and surface area of ​​the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″.
  12. Mast
    stoziar Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'.
  13. Rectangle
    golden-rectangle-ratio Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
  14. Earth parallel
    parallels Earth's radius is 6378 km long. Calculate the length parallel of latitude 50°.
  15. Diagonal
    krychle Determine the dimensions of the cuboid, if diagonal long 16 dm has angle with one edge 66° and with other edge 71°.
  16. Rotation of the Earth
    earth_1 Calculate the circumferential speed of the Earth's surface at a latitude of 53.7°​​. Consider a globe with a radius of 6378 km.
  17. Rotary cone
    cone_3 The volume of the rotation of the cone is 104 cm3 and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.
  18. Cuboid
    cuboid_diagonal Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60°
  19. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  20. Steeple
    church_tower Steeple seen from the road at an angle of 57°. When we zoom out to 25 meters, it is seen at an angle of 21°. What is high?

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