Planimetrics - problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

  1. The mast
    geodet_1 The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
  2. Three points
    abs1_1 Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
  3. On line
    primka On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
  4. Center of line segment
    stredna_priecka_1 Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
  5. Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  6. An equilateral
    goat__wolf_and_cabbage_1 An equilateral triangle with a side 10 m represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat?
  7. Distance problem 2
    geodetka_1 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
  8. Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  9. The perimeter 2
    quadrilateral_1 The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m?
  10. Square
    namestie_tr_iso Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
  11. AP RT triangle
    right_triangle_4 The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
  12. KLMN trapezoid
    lich_1 In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
  13. Diagonals of pentagon
    5gon_diagonal Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
  14. Sss triangle
    8_11_12 Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
  15. Pavement
    chodnik2 Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
  16. The swimmer
    river_3 The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
  17. Paratrooper
    padak After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land fr
  18. Quarter circle
    quarter_circle_1 What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  19. Square metal sheet
    plech_2 Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
  20. Perimeter of square
    stvorec_1 The square has a circumference 17cm. What is its area?

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