Arccosine - high school - practice problems - page 2 of 3
Number of problems found: 42
- Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Perpendicular 7005
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.
- 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? - 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. - 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 is 0.2 meters below the tank's upper side?
- 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) - 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. - 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.
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