Arccosine - practice problems - last page
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 59
- Angles by cosine law
Calculate the size of the angles of the triangle ABC if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem). - 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. - Isosceles 4741
The arm is five times longer than its base in an isosceles triangle. Calculate its interior angles. - 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 figures. - Cuboids
Two separate cuboids with different orientations are 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) - 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[9, 5] L[-4, 8] M[3, 20] 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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