Pythagorean theorem - math word problems

  1. Railways
    railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
  2. Task
    cube_1 I have homework. The cube has an edge 7 cm long and I must find wall and body diagonal.
  3. Tank
    barrel_1 In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
  4. Height UT
    unilateral_triangle How long is height in the equilateral triangle with a side b = 43?
  5. Square
    namestie Rectangular square has side lengths 183 and 244 meters. How many meters will measure the path that leads straight diagonally from one corner to the other?
  6. Q-Exam
    unit_circle If tg α = 0.9, Calculating sin α, cos α, cotg α .
  7. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
  8. Prism
    3b_hranol Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cub
  9. 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.
  10. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
  11. Rhombus and inscribed circle
    rhombus_2 It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
  12. Segment
    segment_AB Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
  13. Vector
    some_vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
  14. Height
    equilateral_triangle Calculate height of the equilateral triangle if its perimeter is 8?
  15. Circumscribing
    thales Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
  16. Climb
    Mazda_RX7_1 On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
  17. Overload
    banking_glider Calculate how many g's (gravity accelerations) feel glider pilot when turning the horizontal circles of radius 148 m flying at 95 km/h. Centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius of rotatio
  18. R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  19. Center
    circle Calculate the coordinates of the circle center: ?
  20. Circle
    kruznica Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0

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Pythagorean theorem is the base for the right triangle calculator.