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

- 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. - 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. - Clock

How many times a day hands on a clock overlap? - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - 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. - IS triangle

Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long. - 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. - 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°. - Railways

Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters. - 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. - 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. - 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'. - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm. - Radians

Convert 270° to radians. Write result as multiple of number π. - Arc

Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle? - 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? - Gear wheels

Two gear wheels, which fit together have the number of teeth z_{1}=58 and z_{2}=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute. - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 33 and corresponding angle is ?.

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