# Goniomentry and trigonometry - math word problems

1. Pentagon Calculate the area of regular pentagon, which diagonal is u=17.
2. Mast Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'.
3. Rectangle Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
4. Maximum area of rhombus Calculate the interior angles at which equilateral rhombus has a maximum area.
5. Earth parallel Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
6. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
7. Kites Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°?
8. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
9. Angles Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
10. Rotation of the Earth Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
11. Cube - angles Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
12. Climb On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
13. Rotary cone The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
14. Triangular prism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
15. 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°?
16. Equilateral triangle How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
17. Hexagon A Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
18. 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? 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%. Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.