9th grade (14y) + Pythagorean theorem - examples

Pythagorean theorem is the base for the right triangle calculator.

  1. Square pyramid
    pyramid_4 Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
  2. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  3. 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.
  4. 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!
  5. Acceleration 2
    car_14 if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
  6. Quadrilateral 2
    quadrilateral Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
  7. Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  8. Right triangle trigonometrics
    triangle2 Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
  9. Forces on earth directions
    compass2_1 A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object?
  10. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  11. Logs
    gulatina Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm?
  12. Right Δ
    ruler Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
  13. 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.
  14. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm.
  15. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  16. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 200 cm.
  17. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 55 dm.
  18. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 18 cm.
  19. Circle chord
    circleChord What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm?
  20. Acreage
    parcela What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?

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