Arccosine - math word 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. 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.
3. Triangle Triangle KLM is given by plane coordinates of vertices: K[14, -2] L[8, 13] M[-1, -18]. Calculate its area and itsinterior angles.
4. IS triangle Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
5. Angle between vectors Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
6. 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.
7. Sphere in cone A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
8. Trigonometry If you know that cos(γ) = sin (806°), what is the angle γ?
9. Horizontal Cylindrical Segment How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
10. Angle of deviation The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
11. Greatest angle Calculate the greatest triangle angle with sides 197, 208, 299.
12. Gon functions Decide which of the numbers (values ​​of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1.
13. Four sides of trapezoid In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
14. Cylinder horizontally The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
15. Ratio iso triangle The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
16. Right triangle eq2 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
17. Cuboids Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
18. Isosceles triangle 8 If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
19. Calculate 2 Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
20. Substitution method Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2

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