Right triangle - examples - page 27

  1. Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  2. The perimeter
    hexagon6 The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
  3. Equilateral triangle
    vpisany_stvorec A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
  4. Rectangular trapezoid
    right-trapezium-figure The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the.
  5. Equilateral triangle
    equilateral_triangle2_1 Calculate the area of an equilateral triangle with circumference 72cm.
  6. Bamboo
    Bambus Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
  7. 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
  8. Coordinate axes
    tr_triangle_axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
  9. Diagonal to area
    rectangle_5 Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
  10. Quadrangular pyramid
    jehlan_4b_obdelnik_1 Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
  11. Ellipse
    elipsa Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
  12. Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
  13. Is right triangle or not
    triangle_rt1_2 If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
  14. Body diagonal
    diagonal_1 Calculate the length of the body diagonal of the 6cm cube.
  15. Is right-angled
    rt_sqrt_2 Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle?
  16. Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  17. 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?
  18. Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  19. Find radius
    numbers_49 Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
  20. Cone 15
    cone_9 The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?

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