Pythagorean theorem - math word problems

  1. Diameter
    diameter_circle If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
  2. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  3. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  4. Round table
    obrus-kruhovy Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes?
  5. Trapezoid ABCD
    trapezoid_2 Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20.
  6. Circle section
    circle_segment Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector
  7. Axial section
    cylinder_cut Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
  8. RT 10
    triangles_rt Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
  9. OPT
    right_triangle_pythagoras What is the perimeter of a right triangle with the legs 14 cm and 21 cm long?
  10. Square side
    square_analytic_geometry Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
  11. Horizon
    lighthouse The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
  12. Center of the cube
    center_of_cube Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
  13. Elevation
    horizon_diagram What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
  14. Euklid4
    euclid_2 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
  15. Unit vector 2D
    one_1 Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
  16. Rectangle
    golden-rectangle-ratio Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
  17. Column
    pole_phone Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?
  18. Circle chord
    tetiva Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
  19. Rhombus
    rhombus2_3 The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides.
  20. Similarity coefficient
    eqlateral_triangles The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.

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Pythagorean theorem is the base for the right triangle calculator.