Geometry - problems

  1. Air thermal
    air_temperature Imagine that a unit of air rises at 3000 meters high, if temperature decreases 6 degrees celcius for every 1000 meter, what will be its temperature at 1400 meters, 2000 meters, 2500 meters and when it reaches the 3000 meter elevation. Starting temperature.
  2. Distance of lines
    kvadr_2 Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
  3. Pyramid cut
    ihlan_rez We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
  4. Find the 5
    distance-between-point-line Find the equation with center at (1,20) which touches the line 8x+5y-19=0
  5. Two people
    crossing Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar
  6. 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.
  7. 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 ?
  8. Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
  9. Railways
    railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
  10. 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?
  11. 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°?
  12. 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....
  13. 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?
  14. 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.
  15. 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 hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
  16. 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].
  17. 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.
  18. OK circle
    circles2 Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
  19. Climb
    scenic_road Road has climbing 1:27. How big is a angle corresponds to this climbing?
  20. Angle between lines
    angle_two_lines Calculate the angle between these two lines: ? ?

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