Geometry - problems - page 6

1. Rhombus ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
2. Vector Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
3. Triangle SSA Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
4. Medians in triangle Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm.
5. Right angled triangle 2 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
6. Right triangle - leg Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg.
7. Tangents construct Circle is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions has the task?
8. Three points Mark three points E, F and G in the plane not lie on one line. a) Draw a line segment FG b) Construct halfline (ray) EG c) Draw a line EF
9. Mine What is temperature in the mine at a depth of 1160 m, where at depth 9 m is 11°C and every 100 m, the temperature increases by 0.7°C?
10. Line segment For the line segment whose endpoints are L[-1, 13] and M[18, 2], find the x and y value for the point located 4 over 7 the distance from L to M.
11. Three vectors The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
12. Parabola Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
13. Center of gravity The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [14; -2; 5] m1 = 10.2 kg A2 [-2; -16; 7] m2 = 13.6 kg A3
14. Traffic laws Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
15. Clock face clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
16. Inscribed circle Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
17. Square ABCD Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
18. Square Draw a square on the edge of a = 4 cm. Mark the center of symmetry S and all axes of symmetry. How many axes of symmetry does? Write down. The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)? Write an equation of a line parallel to To 9x + 3y = 8 That Passes Through The Point (-1, -4). Write in form ax+by=c.