Cosine - examples
- Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
- Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees
- 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.
In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
- IS triangle
Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
Triangle KLM is given by plane coordinates of vertices: K[-2, -20] L[4, 1] M[-16, 4]. Calculate its area and itsinterior angles.
Calculate the area of regular pentagon, which diagonal is u=19.
Calculate volume and surface area of the cone with diameter of the base d = 19 cm and side of cone with the base has angle 48°36'.
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°.
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
- Earth parallel
Earth's radius is 6375 km long. Calculate the length parallel of latitude 10°.
Determine the dimensions of the cuboid, if diagonal long 31 dm has angle with one edge 61° and with other edge 52°.
- 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 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
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: ? ?