Arccosine - practice problems - last page

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 54

Horizontal Cylindrical Segment
How much fuel is in the horizontal cylindrical segment tank with a length of 10m, a width of level 1 meter, and a level of 0.2 meters below the tank's upper side?
Triangle sides to angles
The triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the sizes of the angles and the area of this triangle.
Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (6, 22) and v = (10, -11)

Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone.
Gon functions
Decide which numbers (values of trigonometric functions) are positive or negative (or zero). Positive mark +1 and negative -1.
Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles.
Greatest angle
Calculate the greatest triangle angle with sides 124, 323, 302.
IS triangle
Calculate the interior angles of the isosceles triangle with base 12 cm and legs 19 cm long.

Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
Forces
In point, G acts three orthogonal forces: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant of F and the angles between F and forces F₁, F₂, and F₃.
Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 5a +5b = 7c
Trigonometry
If you know that cos(γ) = sin (806°), what is the angle γ?
Right triangle
Calculate the unknown side b and interior angles, perimeter, and area of a right triangle if a=10 cm and hypotenuse c = 16 cm.

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