Cosine - examples
- The mast
A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
- 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 19 cm and 80 cm long and angle them clamped is 90°.
- Regular 5-gon
Calculate area of the regular pentagon with side 11 cm.
In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
- IS triangle
Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long.
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles.
Calculate the area of regular pentagon, which diagonal is u=14.
Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'.
Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″.
Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
- Earth parallel
Earth's radius is 6378 km long. Calculate the length parallel of latitude 50°.
Determine the dimensions of the cuboid, if diagonal long 16 dm has angle with one edge 66° and with other edge 71°.
- Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 53.7°. Consider a globe with a radius of 6378 km.
- Rotary cone
The volume of the rotation of the cone is 104 cm3 and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.
Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60°
- Angle between lines
Calculate the angle between these two lines: ? ?