# Arctangent - examples

- Road

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

From the observatory 15 m high and 39 m from the river bank, river width appears in the visual angle φ = 22°. Calculate width of the river. - Descent of road

Road sign informs the gradient is 10.5%. Calculate the angle which average decreases. - Angle between lines

Calculate the angle between these two lines: ? ? - Cube - angles

Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base. - 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. - Climb

Road has climbing 1:23. How big is a angle corresponds to this climbing? - Road

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

Calculate the angle of two lines y=-3x+25 and y=x-3 - 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? - Stairway

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

Calculate the length of the belt on pulleys with diameters of 144 mm and 332 mm at shaft distance 197 mm. - 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. - Bevel

I have bevel in the ratio 1:6. What is the angle and how do I calculate it? - 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. - 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. - 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 - 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. - Height difference

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

Do you have interesting mathematical example that you can't solve it? Enter it and we can try to solve it.