Angle - 8th grade (13y) - examples
- Supplementary angles
One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
- Special watch
Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°?
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.
Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
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 dm2. Calculate the volume of a cone.
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. 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.
- Slope of track
Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitra (167 m AMSL), if the track is 77 km long.
Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°.
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.
Convert 270° to radians. Write result as multiple of number π.
Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
- Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
- Climb in percentage
The height difference between points A and B is 587 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 4.8 km.