Geometry - problems - page 4

1. Unit vector 2D Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
2. Diameter If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
3. Euclid theorems Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
4. Map 2 At what scale is made map if the distance 8.2 km corresponds on the map segment 5 cm long?
5. Airplane Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
6. Vector sum The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
7. Construct 1 Construct a triangle ABC, a = 7 cm, b = 9 cm with right angle at C, construct the axis of all three sides. Measure the length of side c (and write).
8. Vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
9. Trapezoid IV In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD? 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
11. Square side Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
12. Similarity of squares The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ? Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
14. 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
15. The angle of lines Calculate the angle of two lines y=x-21 and y=-2x+14
16. Angle A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
17. 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).
18. 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.
19. Circles How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
20. 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.

Do you have an interesting mathematical problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.