# Geometry - math word problems

1. Rectangular triangles The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c
2. The angle of lines Calculate the angle of two lines y=x-21 and y=-2x+14
3. Angle A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
4. Circles In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
5. Inclined plane On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane.
6. Circles How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
7. Cosine Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544. Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
9. Line How many parts of line divide 5 (different) points that lie on it?
10. Diagonal in rectangle In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
12. Tachometer Tatra's tachometer shows the initial state 886123 km this morning. Tatra today travel at an average speed of 44 km/h. Determine the function that describes the Tatra's tachometer depending on the time. What is the state of tachometer after 4 hours?
13. See harmonics It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
14. Distance Wha is the distance between the origin and the point (18; 22)?
15. Slope What is the slope of the line defined by the equation -2x +3y = -1 ?
16. 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
17. Plane On how many parts divide plane 6 parallels?
18. Circle tangent It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
19. Angle in RT Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
20. Garage There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag

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