# Examples for secondary school students - page 10

1. Angle between lines Calculate the angle between these two lines: ? ?
2. n-gon Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
3. Stairway What angle rising stairway if step height in 17 cm and width 27 cm?
4. Climb Road has climbing 1:27. How big is a angle corresponds to this climbing?
5. Goat and circles What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
6. Tetrahedral pyramid Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
7. Square 2 Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
8. Dice How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
9. Rotary cone Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
10. Sale If the product twice price cut by 25%, what percentage was price cut in total?
11. Square grid Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
12. Football league In the 5th football league is 10 teams. How many ways can be filled first, second and third place?
13. Triangular pyramid Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
14. 4s pyramid Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
15. Circle section Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
16. Angle between vectors Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
17. Cut and cone Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
18. Jewel Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
19. Hypotenuse and height In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
20. RT - hypotenuse and altitude Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?

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