Goniomentry and trigonometry - problems

  1. Calculate 2
    t_sss Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
  2. Substitution method
    500px-Sine_cosine_plot.svg Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
  3. Pilot
    aircraft-02_12 How high is the airplane's pilot to see 0.001 of Earth's surface?
  4. Diagonals of the rhombus
    kosostvorec_3 How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
  5. 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.
  6. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  7. 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°.
  8. 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.
  9. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  10. 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?
  11. 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.
  12. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  13. 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.
  14. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
  15. 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.
  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. 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.
  18. Pentagon
    5gon_3 Calculate the area of regular pentagon, which diagonal is u=17.
  19. 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°.
  20. 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.

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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.