# Cosine - high school - examples

- Substitution method

Solve goniometric equation: sin^{4}θ - 1/cos^{2}θ=cos^{2}θ - 2 - 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. - Trigonometric functions

In right triangle is: ? Determine the value of s and c: ? ? - Triangle SAS

Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°. - Regular 5-gon

Calculate area of the regular pentagon with side 7 cm. - 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}. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°. - Pentagon

Calculate the area of regular pentagon, which diagonal is u=17. - Mast

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 25 dm has angle with one edge 68° and with other edge 63°. - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - Cuboid

Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58° - Angle between lines

Calculate the angle between these two lines: ? ? - Angle between vectors

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

Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high? - 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. - Two forces

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

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