Angle + length - math problems

  1. Hands
    soviet_watch The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
  2. River
    kongo_river Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
  3. Clock
    hodiny How many times a day hands on a clock overlap?
  4. River
    river From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
  5. 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?
  6. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
  7. 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.
  8. Climb in percentage
    12_percent_stupanie The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.
  9. Mast
    stoziar Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'.
  10. Earth parallel
    parallels Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
  11. Diagonal
    krychle Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
  12. Gear wheels
    gear Two gear wheels, which fit together have the number of teeth z1=58 and z2=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute.
  13. Angles
    rhombus_1 Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
  14. Quarter circular
    quarter_circle The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.
  15. Tower
    cone_roof How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
  16. 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.
  17. Cuboid
    cuboid_diagonal Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
  18. Clocks
    clocks How long path will walk the end of the clock's minute-hand long 7 cm for 330 minutes? How long will walk in the same time hour-hand?
  19. Building
    Taipei_101 How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
  20. Airplane navigation
    triangle_airplane An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?

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