Angle + length - math problems

1. Hands The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
2. River Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
3. Clock How many times a day hands on a clock overlap?
4. River From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
5. Observer The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
6. IS triangle Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
7. Slope of track Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long.
8. Climb in percentage The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.
9. Mast Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'.
10. Earth parallel Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
11. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
12. Gear wheels Two gear wheels, which fit together have the number of teeth z1=58 and z2=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute.
13. Angles Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
14. Quarter circular The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.
15. Tower How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°? Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
17. Cuboid Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
18. Clocks How long path will walk the end of the clock's minute-hand long 7 cm for 330 minutes? How long will walk in the same time hour-hand?
19. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°? An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?