# Arccosine - math word problems

- 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. - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Triangle

Triangle KLM is given by plane coordinates of vertices: K[14, -2] L[8, 13] M[-1, -18]. Calculate its area and itsinterior angles. - IS triangle

Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long. - Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20) - Right triangle

Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm. - Sphere in cone

A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions. - Trigonometry

If you know that cos(γ) = sin (806°), what is the angle γ? - 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? - 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. - Greatest angle

Calculate the greatest triangle angle with sides 197, 208, 299. - 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. - 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. - 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? - 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. - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - 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) - 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

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