Pythagorean theorem - math word problems

  1. Catheti
    pyt_theorem The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
  2. Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  3. Euclidean distance
    euclidean Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
  4. RT 11
    right_triangle Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
  5. Ladder
    studna 8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
  6. Distance
    origin_math Wha is the distance between the origin and the point (18; 22)?
  7. Vectors
    vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
  8. Leg
    tetris Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
  9. Inscribed rectangle
    circle_desc_rectangular The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
  10. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  11. 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?
  12. Angle between vectors
    arccos Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
  13. 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.
  14. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  15. 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?
  16. 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.
  17. 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
  18. 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.
  19. 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.
  20. OPT
    right_triangle_pythagoras What is the perimeter of a right triangle with the legs 14 cm and 21 cm long?

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Pythagorean theorem is the base for the right triangle calculator.