Angle - 8th grade (13y) - examples

  1. ABCD square
    s1 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?
  2. Tetrahedron
    3sidespyramid What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
  3. Hands
    soviet_watch 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.
  4. River
    kongo_river Calculate how many promiles river Vltava average falls, if on section long 695 km flowing water from 1601 m AMSL to 183 m AMSL.
  5. Clock
    hodiny How many times a day hands on a clock overlap?
  6. Is right?
    rtriangle Is triangle with sides 24, 51 and 45 right triangle?
  7. River
    river 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.
  8. Cone A2V
    popcorn 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.
  9. IS triangle
    isoscelestriangle-pic Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long.
  10. Cuboid diagonal
    cube_2 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.
  11. Slope of track
    sklon_1 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.
  12. Cone
    cone-blue 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″.
  13. Mast
    stoziar 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'.
  14. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  15. Rectangle
    golden-rectangle-ratio Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
  16. Isosceles right triangle
    3triangles Calculate the area of an isosceles right triangle whose perimeter is 236 dm.
  17. Radians
    pi_text Convert 54° to radians. Write result as multiple of number π.
  18. Arc
    arc_1 Circle arc corresponding to angle is 193° is 23 dm long. What is the length of the entire circle?
  19. Quarter circular
    quarter_circle The wire that is hooked around the perimeter of quarter-circular arc has length 14π+56. Determine the radius of circle arc.
  20. Circular pool
    arc_open 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?

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