Cosine - examples
- Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
- Angle of deviation
The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
- 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.
- Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
The point (21, 20) is on the terminal side of angle θ. cos θ = ?
- Side c
In △ABC a=3, b=8 and ∠C=70°. Calculate length of the side c.
- Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
- Circular sector
I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
- Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16)
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
- Regular 5-gon
Calculate area of the regular pentagon with side 11 cm.
- Triangle TBC
TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB?
If you know that cos(α) = sin (-968°), what is the angle α?
- Angle between lines
Calculate the angle between these two lines: ? ?
Steeple seen from the road at an angle of 57°. When we zoom out to 25 meters, it is seen at an angle of 21°. What is high?
- Earth parallel
Earth's radius is 6378 km long. Calculate the length parallel of latitude 50°.
- House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 52° and we calculate 9% of waste, connections and overlapping of area roof?
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 19 and 4 and with the hypotenuse 19.416.
Calculate how much land saw Felix Baumgartner after jump from 22 km above ground. The radius of the Earth is R = 6378 km.
Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.