# Arccosine - math word problems

- 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 is to interconnect 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? - 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: sin^{4}θ - 1/cos^{2}θ=cos^{2}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 cm^{2}(with circle base), its surface area is 20 cm^{2}. 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 tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank? - Sphere in cone

A sphere of radius 3 cm desribe 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) - Gon functions

Decide which of the numbers (values of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1. - Greatest angle

Calculate the greatest triangle angle with sides 197, 208, 299. - Triangle

Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles. - IS triangle

Calculate interior angles of the isosceles triangle with base 46 cm and legs 49 cm long. - Trapezoid MO

The rectangular trapezoid ABCD with 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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