Pythagorean theorem - problems - page 2

  1. Movement
    peleton From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 16 km/h. Determine the distance between them after 35 minutes cycling.
  2. Square
    square_1 Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  3. Is right?
    rtriangle Is triangle with sides 51, 56 and 77 right triangle?
  4. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
  5. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
  6. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
  7. Cone A2V
    popcorn 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.
  8. River
    river 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.
  9. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 33 km.
  10. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 38 cm and 55 cm long.
  11. Logs
    gulatina Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
  12. Square and circles
    kruznica_stvorec_1 Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  13. Rectangle
    diagonal In rectangle with sides 3 and 10 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
  14. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  15. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD.
  16. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
  17. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  18. Widescreen monitor
    lcd Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of ​​the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
  19. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
  20. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.

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Pythagorean theorem is the base for the right triangle calculator.