Pythagorean theorem - problems - page 6

  1. V-belt
    v_belt Calculate the length of the belt on pulleys with diameters of 113 mm and 308 mm at shaft distance 190 mm.
  2. Rotating cone II
    cone Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
  3. Prism
    prism-square The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
  4. Arm
    arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 18 cm and a height v=17 cm.
  5. Airplane navigation
    triangle_airplane An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
  6. Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
  7. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  8. Q-Exam
    unit_circle If tg α = 0.9, Calculating sin α, cos α, cotg α .
  9. Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  10. Two balls
    balls-inside-cylinder Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
  11. Equilateral triangle
    unilateral_triangle Calculate the side of an equilateral triangle, if its area is 892 mm2.
  12. Vector
    some_vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
  13. Euklid4
    euclid_2 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
  14. Sphere and cone
    cone_in_sphere Within the sphere of radius G = 36 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
  15. Pit
    ihlan_zrezany Pit has shape of a truncated pyramid with rectangular bases and is 3.5 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.8 l of green colour. How many liters of paint is needed when w
  16. Elevation
    horizon_diagram What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
  17. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  18. Sea
    ship How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
  19. Hexagonal prism
    hexa_prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
  20. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.

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Pythagorean theorem is the base for the right triangle calculator.