Arctangent - examples
- 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.
From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river.
- Slope of track
Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long.
- 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 3 km long of rise average 4‰. Calculate the height difference of cities A and B.
What angle rising stairway if step height in 17 cm and width 24 cm?
Road has climbing 1:23. How big is a angle corresponds to this climbing?
- Angle between lines
Calculate the angle between these two lines: ? ?
Pyramid has a base a = 9cm and height in v = 15 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
Calculate the length of the belt on pulleys with diameters of 162 mm and 454 mm at shaft distance 425 mm.
- 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.
Average climb of the road is given by ratio 1:29. By what angle road average climb?
- Slope of the pool
Calculate slope (rise:run) of the bottom of swimming pool long 40 m. Water depth at beginning of pool is 1.15 m (for children) and depth at end is 1.92 m (for swimmers). Slope express as percentage and as angle in degrees.
- Descent of road
Road sign informs the gradient is 10.5%. Calculate the angle which average decreases.
- Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?
- Glass of juice
Glass of juice shaped cylinder 16 cm height and base diameter of 10 cm is filled with juice so that the level is 3 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.
- Map - climb
On the map of High Tatras in scale 1:25000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 156 mm. Altitude of this stations are 944 m and 1755 m. What is average angle of climb of this cable car track?
On the pedestal high 2.3 m is statue 3.3 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 1.5 m.
Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent?
- Goniometric form
Determine goniometric form of a complex number ?.