Geometry - problems

  1. Points on line segment
    segment Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
  2. Right angled triangle 2
    vertex_triangle_right LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n
  3. Line segment
    lines_5 Cut a line segment of 15 cm into two line segments so that their lengths are in ratio 2:1. What length will each have?
  4. Forces
    ijk In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 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: 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. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles.
  7. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  8. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
  9. 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?
  10. Hexagon
    hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 19, 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 20%. 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 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of ​​the larger triangle.
  13. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12].
  14. Speed of Slovakian trains
    zssk_train Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37
  15. Climb
    scenic_road Road has climbing 1:23. How big is a angle corresponds to this climbing?
  16. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 43 and one cathetus long 21.
  17. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?
  18. Height
    thales_law Is right that in any right triangle height is less or equal half of the hypotenuse?
  19. 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.
  20. Slope
    slope What is the slope of a line with an inclination 52°?

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