Angle - 8th grade (13y) - examples
- ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
The clock shows 12 hours. After how many minutes will agle between hour and minute hand 80°? Consider the continuous movement of both hands hours.
Calculate how many promiles river Vltava average falls, if on section long 695 km flowing water from 1601 m AMSL to 183 m AMSL.
How many times a day hands on a clock overlap?
- Is right?
Is triangle with sides 24, 51 and 45 right triangle?
From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river.
- 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.
- IS triangle
Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.
- Slope of track
Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long.
Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″.
Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'.
Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
- Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 236 dm.
Convert 54° to radians. Write result as multiple of number π.
Circle arc corresponding to angle is 193° is 23 dm long. What is the length of the entire circle?
- Quarter circular
The wire that is hooked around the perimeter of quarter-circular arc has length 14π+56. Determine the radius of circle arc.
- 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?