Geometry - problems - page 4
- Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
- 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.
- Map 2
At what scale is made map if the distance 8.2 km corresponds on the map segment 5 cm long?
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
- 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?
- 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).
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?
- 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?
- Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
- 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: ?
- Shadow and light
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?
- 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
- The angle of lines
Calculate the angle of two lines y=x-21 and y=-2x+14
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
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).
- 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.
How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.