Cosine + right triangle - math problems

1. Trapezoid MO The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
2. Trigonometric functions In right triangle is: ? Determine the value of s and c: ? ?
3. Triangle SAS Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
4. Regular 5-gon Calculate area of the regular pentagon with side 7 cm.
5. Forces In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
6. Right Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
7. IS triangle Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
8. Cone Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
9. Pentagon Calculate the area of regular pentagon, which diagonal is u=17.
10. 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'.
11. Rectangle Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
12. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
13. 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.
14. 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.
15. Steeple Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
16. Right triangle Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
17. Two forces Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
19. House roof The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
20. EQL triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.

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