Pythagorean theorem - examples - page 8

  1. Cuboid
    cuboid_3 Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
  2. Horizon
    lighthouse The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
  3. Oil rig
    oil_rig_tower Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
  4. Rhombus base
    paral_prism Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 10 cm. Prism height is twice base edge length.
  5. Pine wood
    dre-borovica From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum
  6. Nice prism
    diagonal_rectangular_prism.JPG Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
  7. Sphere - parts
    odsek_vusek Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
  8. Height
    equilateral_triangle Calculate height of the equilateral triangle if its perimeter is 8?
  9. Rectangle
    obdelnik_1 The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
  10. Chord
    chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
  11. Task
    cube_1 I have homework. The cube has an edge 7 cm long and I must find wall and body diagonal.
  12. Isosceles trapezoid
    licho_1 Calculate the area of an isosceles trapezoid whose bases are in the ratio of 4:3; leg b = 13 cm and height = 12 cm.
  13. Right trapezoid
    lich_right The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length 0.25 dm. Calculate the lengths of the diagonals and the second leg.
  14. Angle of deviation
    kuzel2_1 The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
  15. Arc
    arc Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
  16. Column
    pole_phone Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?
  17. Triangular pyramid
    ihlan_3b It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
  18. Circle
    talesova On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
  19. Rectangle - desc circle
    obdelnik_kruh Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter.
  20. Hexagonal pyramid
    hexagonal-pyramid Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.

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Pythagorean theorem is the base for the right triangle calculator.