# Angle - 8th grade (13y) - math problems

1. Hands The clock shows 12 hours. After how many minutes will angle between the 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. Is right? Is triangle with sides 51, 56 and 77 right triangle?
5. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
6. 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.
7. IS triangle Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
8. Cuboid diagonal Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
9. Cone Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
10. Railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
11. 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.
12. 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.
13. 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'.
14. Rectangle Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
15. Isosceles right triangle Calculate the area of an isosceles right triangle whose perimeter is 377 cm. Convert 270° to radians. Write result as multiple of number π.
17. Arc Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
18. Circular pool The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
19. 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.
20. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.

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