Goniomentry and trigonometry - math word problems

  1. Cable car
    lanovka Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
  2. Glass of juice
    glass_of_juice Glass of juice shaped cylinder 16 cm height and base diameter of 7 cm is filled with juice so that the level is 4 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.
  3. Descent of road
    znacka_klesanie Road sign informs the gradient is 10.3%. Calculate the angle which average decreases.
  4. Black building
    talapka_cierna_stavba Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchi
  5. Kites
    drake Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°?
  6. Maximum area of rhombus
    rhombus Calculate the interior angles at which equilateral rhombus has a maximum area.
  7. Jewel
    rhombus3 Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
  8. Road
    cesta Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
  9. Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  10. Cube - angles
    cube_diagonal_1 Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
  11. Triangle SAA
    triangle_blue The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
  12. Slope of track
    sklon_1 Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long.
  13. Rotation of the Earth
    earth_1 Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
  14. 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.

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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.