Arctangent - practice problems - last page
Number of problems found: 92
- River
From the observatory 18 m high and 31 m from the riverbank, river width appears in the visual angle φ = 20°. Calculate the width of the river. - Trapezoid MO
Right-angled trapezoid ABCD has a right angle at vertex B. Given that |AC| = 12, |CD| = 8, and the diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Climb
A road has a gradient of 1:26. What angle of inclination does this correspond to? - Statue
On the pedestal, high 4 m is a statue 2.7 m high. At what distance from the statue must the observer stand to see it at the maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m. - Angle between lines
Calculate the angle between the following two lines: p: -4x +7y +7 =0 q: -x +4y +7=0 - The angle of lines
Calculate the angle between the two lines y = x-8 and y = +12. - V-belt
Calculate the length of a belt running on two pulleys with diameters of 105 mm and 393 mm, with a centre-to-centre distance of 697 mm. - Glass of juice
A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling. - Descent of road
A road sign shows a gradient of 10.9%. Calculate the angle of inclination of the slope. - Road
Between cities A and B there is a route 9 km long with an average gradient of 9‰ klesanie. Calculate the height difference between cities A and B. - Cube - angles
Calculate the angle alpha (α) between the face diagonal and the base of a cube. Calculate the angle beta (β) between the space diagonal and the base of the cube. - Slope of track
Calculate the average gradient (in per mille and in degrees) of the railway tracks between Prievidza (309 m above sea level) and Horná štubňa (624 m above sea level), given that the track is 37 km long.
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