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

Pythagorean theorem is the base for the right triangle calculator.

  1. 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.
  2. 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.
  3. 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)
  4. 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?
  5. Center of gravity
    triangles_9 In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
  6. Isosceles triangle
    triangles_8 Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
  7. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  8. Logs
    gulatina Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm?
  9. 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.
  10. 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.
  11. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm.
  12. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  13. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 200 cm.
  14. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 55 dm.
  15. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  16. 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?
  17. Acreage
    parcela What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
  18. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
  19. Circumscribing
    thales Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 3 cm.
  20. Garden
    garden_1 Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden?

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