Right triangle - problems

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  1. Rectangle
    rectangle_inscribed_circle The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle.
  2. Square and circles
    kruznica_stvorec_1 Square with sides 41 m is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  3. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  4. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 200 cm.
  5. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
  6. Rhombus
    rhomus_circle It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  7. Kites
    drake Boys run kite on a cable of 86 meters long. What is the kite altitude, if the angle from the horizontal plane is 77°?
  8. Isosceles right triangle
    3triangles Calculate the area of an isosceles right triangle whose perimeter is 236 dm.
  9. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel.
  10. 4s pyramid
    pyramid_regular Regular tetrahedral pyramid has a base edge a=6 and collaterally edge length b=15. What is its height?
  11. n-gon II
    x-gon_1 What is the side length of the regular 9-gon circumscribed circle of radius 13 cm?
  12. Crossroads
    crossroad The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car.
  13. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  14. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=13 cm, vb=17 cm and side b is 5 cm shorter than side a.
  15. Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
  16. Aircraft
    aircraft The plane flies at altitude 6800 m. At the time of first measurement was to see the elevation angle of 20° and second measurement of the elevation angle of 34°. Calculate the distance the plane flew between the two measurements.
  17. Triangle TBC
    isosceles_triangle TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB?
  18. Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 20 cm, R = 21 cm (R is the circumradius).
  19. Diamond
    cerveny_kosoctverec Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
  20. Above Earth
    aboveEarth To what height must a boy be raised above the earth in order to see one-fifth of its surface.

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