# 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 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river. - Slope of track

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. - 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 7 km long of fall average 4‰. Calculate the height difference of cities A and B. - Stairway

What angle rising stairway if step height in 17 cm and width 27 cm? - Climb

Road has climbing 1:27. 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 = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges. - 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. - V-belt

Calculate the length of the belt on pulleys with diameters of 113 mm and 308 mm at shaft distance 190 mm. - Slope of the 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. - Road

Average climb of the road is given by ratio 1:15. By what angle road average climb? - 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. - 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 10.3%. Calculate the angle which average decreases. - 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? - Railway

Railway line had on 5.8 km segment climb 9 permille. How many meters track ascent? - 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. - 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

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