Arccosine - practice problems - page 2 of 3
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 59
- Two forces 3
Two forces with magnitudes 8 Newtons and 15 Newtons act at a point. Find the angle between the forces if the resultant force is 17 Newtons. - A rectangle 5
A rectangle has sides of 10 cm and 14 cm. Calculate the angle between a diagonal and a long side. - Space vectors 3D
The vectors u = (1; 3;- 4) and v = (0; 1; 1) are given. Find their sizes, calculate their angles, and determine the distances between them. - Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - The angle of view
Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - The aspect ratio
The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle.
- Circular railway
The railway connects points A, B, and C in a circular arc, whose distances are | AB | = 30 km, AC = 95 km, and BC | = 70 km. How long will the track be from A to C? - Roof angle
The house's roof has the shape of an isosceles triangle with arms 4 m long and the size of the base 6 m. How big an angle alpha does its roof make? - Isosceles triangle 8
If the rate of the sides of an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree. - Calculate 2
Calculate the largest angle of the triangle whose sides are 5.2cm, 3.6cm, and 2.1cm - Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Perpendicular direction
A speedboat moves relative to the water at a constant speed of 13 m/s. The speed of the water current in the river is 5 m/s a) At what angle concerning the water current must the boat sail to keep moving perpendicular to the banks of the river? b) At what - Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Parametrically 6400
Find the angle of the line, which is determined parametrically x = 5 + t y = 1 + 3t z = -2t t belongs to R and the plane, which is determined by the general equation 2x-y + 3z-4 = 0.
- Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Horizontal watertank
We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. Calculate how many liters of water is in first centimeters. - 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.
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