# Arctangent - problems

- 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. - River

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. - Road

Between cities A and B is route 3 km long of rise average 4‰. Calculate the height difference of cities A and B. - Stairway

What angle rising stairway if step height in 17 cm and width 24 cm? - Climb

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

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. - V-belt

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. - 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. - Road

Average climb of the road is given by ratio 1:29. By what angle road average climb? - 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. - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille? - Descent of road

Road sign informs the gradient is 10.5%. Calculate the angle which average decreases. - 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? - Statue

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

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 ?.

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