Right triangle + expression of a variable from formula - problems

  1. Spherical cap
    gulovy_odsek Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
  2. Rectangle
    rectangle_22 There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
  3. Balloon and bridge
    hlbkovy_angle From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
  4. Rectangular triangle
    rt_triangle_2 The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
  5. Rectangular field
    rectangle_inside_circle_2 A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
  6. Children playground
    lich_5 The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
  7. Quadrangular pyramid
    pyramid_4s_1 The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
  8. Right Δ
    ruler Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
  9. 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.
  10. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  11. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  12. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
  13. R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  14. ISO triangle
    rr Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
  15. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  16. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  17. Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
  18. Perimeter and legs
    RT_triangle Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
  19. 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.
  20. Cathethus and the inscribed circle
    RightTriangleInradius In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.

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