Cosine - problems
- The pond
We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
- 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[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
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°.
Calculate the area of regular pentagon, which diagonal is u=17.
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: ? ?
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)