Goniomentry and trigonometry - problems

  1. Inlet and outlet
    bazen2_19 The pool has a capacity of 50 hl. The inlet pipe flows in 1 minute 1.25 hl, and the waste pipe outlet is draining the full pool in 50 minutes. How long will take the empty the full pool when both the inlet and outlet are opened at the same time?
  2. Two bricks
    bricks_4 One brick weighs 1kg and half a brick, how many weigh two bricks?
  3. Diagonals of pentagon
    5gon_diagonal 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.
  4. 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.
  5. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  6. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
  7. River
    river From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
  8. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  9. Observer
    ohrada The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
  10. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  11. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  12. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
  13. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
  14. Cuboid diagonal
    cube_2 Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
  15. Slope of track
    sklon_1 Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitra (167 m AMSL), if the track is 77 km long.
  16. Cone
    cone-blue Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
  17. Pentagon
    5gon_3 Calculate the area of regular pentagon, which diagonal is u=17.
  18. Mast
    stoziar Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°.
  19. Rectangle
    golden-rectangle-ratio Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
  20. Maximum area of rhombus
    rhombus Calculate the interior angles at which equilateral rhombus has maximum area.

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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.