Arccosine - practice problems
Number of problems found: 37
- Sin cos tan
If cos y = 0.8, 0° ≤ y ≤ 90°, find the value of (4 tan y) / (cos y-sin y)
Loonie has three wooden sticks measuring 17 inches, 21 inches, and 25 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by 17 inches and 21 inches. (Express answers to the nearest hundredths) (using the law of cosines)
- A chord
In a circle radius of 6 cm, a chord is drawn 3 cm from the center. Calculate the angle subtended by the cord at the center of the circle Hence find the length of the minor arc cut off by the chord.
- Two forces 3
Two forces with magnitudes 8 Newtons and 15 Newtons, respectively, act at a point. If the resultant force is 17 Newtons, find the angle between the forces.
- A rectangle 5
A rectangle has sides of 10 cm and 14 cm. Calculate the angle between a diagonal and alongside.
- Space vectors 3D
The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, and the distance between the vectors.
- 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 in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, 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
- 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.
- Horizontal 6161
We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. (only up to a height of 85 cm)
- Toboggan 5710
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?