Geometry - examples

  1. Hypotenuse - RT
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  2. A boy
    angles_6 A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
  3. Shadow of tree
    stromcek_3 Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
  4. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  5. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
  6. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-2, -20] L[4, 1] M[-16, 4]. Calculate its area and itsinterior angles.
  7. Railways
    railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
  8. Circular pool
    arc_open The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  9. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 40° and second one has acute angle 50°?
  10. Hexagon
    hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
  11. Climb
    Mazda_RX7_1 On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
  12. Similarity coefficient
    eqlateral_triangles The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
  13. Speed of Slovakian trains
    zssk_train Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava
  14. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
  15. Crossroads
    crossroad The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
  16. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
  17. Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  18. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  19. Pentagon
    5gon_1 Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
  20. The chord
    Tetiva Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?

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