Arctangent - examples

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Road
    cesta Between cities A and B is route 7 km long of fall average 4‰. Calculate the height difference of cities A and B.
  6. Stairway
    steps What angle rising stairway if step height in 17 cm and width 27 cm?
  7. Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  8. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  9. Pyramid
    jehlan Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
  10. Two forces
    vector-add Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
  11. V-belt
    v_belt Calculate the length of the belt on pulleys with diameters of 113 mm and 308 mm at shaft distance 190 mm.
  12. Slope of the pool
    swimming_pool Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 0.85 m (for children) and depth at end is 1.73 m (for swimmers). Slope express as percentage and as angle in degrees.
  13. Road
    route-66 Average climb of the road is given by ratio 1:15. By what angle road average climb?
  14. 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.
  15. Height difference
    road What height difference overcome if we pass road 1 km long with a pitch21 per mille?
  16. Descent of road
    znacka_klesanie Road sign informs the gradient is 10.3%. Calculate the angle which average decreases.
  17. Map - climb
    Lanovka_na_skalnate_pleso On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m. What is average angle of climb of this cable car track?
  18. Railway
    train_1 Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
  19. Statue
    michelangelo On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
  20. Sun rays
    sfinga-a-cheopsova-pyramida-w-4066 If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei

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