# Arctangent - high school - examples

1. Trapezoid MO
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
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
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
Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
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
What angle rising stairway if step height in 17 cm and width 27 cm?
7. Climb
Road has climbing 1:27. How big is a angle corresponds to this climbing?
8. Angle between lines
Calculate the angle between these two lines: ? ?
9. Pyramid
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
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
Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
12. Slope of the 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.
Average climb of the road is given by ratio 1:15. By what angle road average climb?
14. Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?
15. Map - climb
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
Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
17. Statue
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.
18. Sun rays
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
19. Goniometric form
Determine goniometric form of a complex number ?.
20. Angle
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.

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