# Pythagorean theorem - problems - page 17

1. Cube
Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
2. Drainage channel
The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
3. Chord distance
The circle k (S, 6 cm), calculate the chord distance from the center circle S when the length of the chord is t = 10 cm.
4. Diamond
Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
5. Bearing
A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
7. Chors centers
The circle with a diameter 17 cm, upper chord /CD/ = 10.2 cm and bottom chord /EF/ = 7.5 cm. The midpoints of the chords H, G is that /EH/ = 1/2 /EF/ and /CG/ = 1/2 /CD/. Determine the distance between the G and H, if CD II EF (parallel).
8. Ethernet cez ulicu
Karol a Jozef sú vášniví hráči počítačových hier a býva v domoch, ktoré sú presne naproti sebe cez ulicu, takže si vidia navzájom do okien. Rozhodli sa, že si svoje počítače prepoja telefónnym káblom aby mohli hrať spoločne hry. Karol býva v prvom poschodí
9. Broken tree
The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
10. Medians and sides
Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
11. The mast
A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
12. Rectangle 3-4-5
The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
13. Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
14. Medians and sides
Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
15. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
16. Two cyclists
Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?
17. Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
18. Pentagon
Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
19. 3s prism
It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.