Arccosine - math word problems

  1. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  2. The aspect ratio
    triangles The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
  3. Circular railway
    described_circle2 The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
  4. Isosceles triangle 8
    7-6-7-triangle If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
  5. Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  6. Substitution method
    500px-Sine_cosine_plot.svg Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
  7. Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  8. 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?
  9. 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.
  10. 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.
  11. 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.
  12. 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=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
  13. 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?
  14. Sphere in cone
    sphere-in-cone A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
  15. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  16. 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.
  17. Greatest angle
    triangles_4 Calculate the greatest triangle angle with sides 197, 208, 299.
  18. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
  19. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 46 cm and legs 49 cm long.
  20. 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.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...