Pythagorean theorem - examples

Pythagorean theorem is the base for the right triangle calculator.

  1. 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.
  2. Cube in sphere
    sphere4 The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
  3. Isosceles triangle
    triangles_8 Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
  4. Is right?
    rtriangle Is triangle with sides 24, 51 and 45 right triangle?
  5. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  6. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  7. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
  8. Triangle
    eq_triangle Can be rectangular triangle equilateral?
  9. Height
    thales_law Is right that in any right triangle height is less or equal half of the hypotenuse?
  10. Logs
    gulatina Trunk diameter is 72 cm. Is it possible to inscribe a square prism with side 54 cm?
  11. 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.
  12. 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.
  13. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 7 cm, b = 6 cm.
  14. Ladder
    rebrik_1 Ladder 5 m long is leaning against the wall. It foot is 0.9 m away from the wall. In which height ladder touch the wall?
  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 91 dm.
  18. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 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. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=29 and height v=27. Calculate the perimeter of the triangle.

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