Arccosine - 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. 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.
  4. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long.
  5. 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.
  6. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
  7. Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  8. Trigonometry
    trigonometry If you know that cos(α) = sin (-968°), what is the angle α?
  9. Sphere in cone
    sphere-in-cone A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
  10. Angle of deviation
    kuzel2_1 The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
  11. Horizontal Cylindrical Segment
    cylinder_horiz How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
  12. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 464, 447, 274.
  13. Gon functions
    quadrants Decide which of the numbers (values ​​of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1.
  14. Four sides of trapezoid
    lichobeznik-stredni_pricka_3 In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
  15. Ratio iso triangle
    iso_triangle_2 The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
  16. Cuboids
    3dvectors Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62149553, 0.11709336, 0.77461762) u2=(0.046501848, 0.66652649, 0.74402958)

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