Arccosine - practice problems - page 3 of 4
Instructions: For each problem, solve carefully and show your complete working.Number of problems found: 65
- Toboggan run
The length of the toboggan run is 60 m, and the height is 8 m. The boy pulls a sled weighing 15 kg. How hard does the boy pull the sled uphill? - 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 cylinder's axis. How many hectoliters of water is in the cylinder? - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - 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. - Triangle angles
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 10 m, 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. - The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (The cone side is the segment joining the vertex cone with any point of the base circle. All sides - Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine the cone's dimensions. - Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (-1, 24) and v = (-8, -21) - 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. - Triangle
Calculate the area of the triangle ABC if b = c = 18 cm, R = 19 cm (R is the circumradius). - 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
Right-angled trapezoid ABCD has a right angle at vertex B. Given that |AC| = 12, |CD| = 8, and the diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
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