Pythagorean theorem - examples

  1. Cross road
    cyclist_34 From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?
  2. Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  3. Slant height
    cone_10 The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
  4. Distance of lines
    kvadr_2 Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
  5. Deviation of the lines
    kvadr_1 Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
  6. Decagon
    decanon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
  7. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  8. Isosceles triangle
    triangle2_3 The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
  9. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  10. Sphere from tree points
    sphere2_1 Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
  11. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  12. Find the 5
    distance-between-point-line Find the equation with center at (1,20) which touches the line 8x+5y-19=0
  13. Two people
    crossing Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar
  14. Garden
    garden_1 Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
  15. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  16. Right Δ
    ruler Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
  17. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 3724 cm3. Determine the length of the edges of a cube.
  18. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  19. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
  20. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.

Do you have interesting mathematical example that you can't solve it? Enter it and we can try to solve it.



To this e-mail address we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.



Pythagorean theorem is the base for the right triangle calculator.