# Arccosine - math problems

#### Number of problems found: 28

• 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), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, 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 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 from A to C?
• Roof angle The roof of the house 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 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 side are 5.2cm, 3.6cm, and 2.1cm
• Substitution method Solve 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.
• 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 axis of the cylinder. How many hectoliters of water is in the cylinder?
• Angle of deviation The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
• 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.
• 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 figure.
• Cuboids Two separate cuboids with different orientation 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, the width of level 1 meter, and the 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 of a degree. u = (-22, 11) and v = (16, 20)

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