Pythagorean theorem - problems

Pythagorean theorem is the base for the right triangle calculator.

  1. 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.
  2. Square
    square_1 Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  3. Medians
    medias_triangle Calculate the sides of a right triangle if the length of the medians to the legs are ta = 23 cm and tb=14 cm.
  4. R Trapezium
    Trapezium_example Rectangular trapezium has bases 17 and 7 and area 80 cm2. What is its perimeter?
  5. Rhombus
    rhombus_1 Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
  6. Triangular prism
    TriangularPrism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 50 degrees, |AB| = 5 cm. Calculate the volume of the prism.
  7. Cut and cone
    kuzel Calculate the volume of the rotation cone which lateral surface is circle arc with radius 14 cm and central angle 66 degrees.
  8. 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.
  9. Euklid4
    euclid_2 Legs of a right triangle have dimensions 61 m and 39 m. Calculate the length of the hypotenuse and the height of this right triangle.
  10. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=100 cm.
  11. Distance
    distance Calculate distance between two points Z[7; -9] and U[-10; -8].
  12. Rhombus base
    paral_prism Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 22 cm and u2 = 15 cm. Prism height is twice base edge length.
  13. 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
  14. Height UT
    unilateral_triangle How long is height in the equilateral triangle with a side c = 7?
  15. Vectors
    vectors Vector a has coordinates (7; 16) and vector b has coordinates (15; -7). If the vector c = b - a, what is the magnitude of the vector c?
  16. Round table
    obrus-kruhovy Round table with diameter d = 95 cm is coated by square tablecloth with a side length 122 cm. About how many cm is higher center of tablecloth than its cornes?
  17. RT leg and perimeter
    rt_1 Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 188.
  18. Semicircle
    semicircle_2 To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
  19. Dig water well
    studna_2 Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out?
  20. Triangle ABC
    squares4 Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?

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