Arctangent + right triangle - 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 Topoľčany (174 m AMSL), if the track is 44 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 13 km long of stúpanie average 7‰. 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. 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.
  9. 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.
  10. V-belt
    v_belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
  11. Slope of the pool
    swimming_pool Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
  12. Road
    route-66 Average climb of the road is given by ratio 1:15. By what angle road average climb?
  13. Height difference
    road What height difference overcome if we pass road 1 km long with a pitch21 per mille?
  14. Descent of road
    znacka_klesanie Road sign informs the gradient is 10.3%. Calculate the angle which average decreases.
  15. 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?
  16. Railway
    train_1 Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
  17. 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
  18. Church tower
    usti-kostel Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
  19. Bevel
    zkoseni I have bevel in the ratio 1:6. What is the angle and how do I calculate it?
  20. V-belt
    remenice-a-remen1 Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm

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