High school + Pythagorean theorem - examples

  1. Vertices of a right triangle
    right_triangle_5 Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle
  2. Infinite sum of areas
    height-of-equilateral-triangle Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
  3. Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  4. Axial cut of a rectangle
    cylinder_cut Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
  5. Diamond diagonals
    kosodlznik_2 Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
  6. Diagonals of a rhombus 2
    rhombus3_4 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
  7. 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.
  8. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 8818 cm3. Determine the length of the edges of a cube.
  9. Axial section
    cone2 Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
  10. 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?
  11. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  12. Trigonometric functions
    trigonom In right triangle is: ? Determine the value of s and c: ? ?
  13. Cuboid
    cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
  14. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
  15. Triangle SAS
    triangle_iron Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
  16. Square
    square_1 Points A[-10,-1] and B[2,-1] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
  17. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
  18. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  19. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 44000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2000 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
  20. River
    river From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.

Do you have an 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.