# Goniomentry and trigonometry - examples - page 3

1. Tower
How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
2. Equilateral triangle
How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
3. Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
4. Regular quadrangular pyramid
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
5. Metallurgical enterprise
Metallurgical company daily produces 318 tons of cast iron. How many tons of coke it burns to melt cast iron when 10 tons of cast consumes 6 tons of coke?
6. Road
Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
7. Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
8. Cuboid
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
9. Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
10. 4side pyramid
Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
11. Building
How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
12. n-gon II
What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
13. Angle between lines
Calculate the angle between these two lines: ? ?
14. Stairway
What angle rising stairway if step height in 17 cm and width 27 cm?
15. Climb
Road has climbing 1:27. How big is a angle corresponds to this climbing?
16. 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
17. 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.
18. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
19. Jewel
Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
20. Rhomboid
Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.

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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.