Goniomentry and trigonometry - examples
- Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
- Bicycle gear
The pedal bicycle wheel has 56 teeth and a rear 20 gear tooth. How many times does the bicycle wheel turn when you make 20 turns of the pedal wheel?
School kitchen bought 36kg apples for 12 kc/kg. How many kilograms of apples 1/4 cheaper can they buy for the same money?
- Proportion 2
A car is able to travel 210 km in 3 hours. How far can it travel in 5 hours? Put what kind of proportion is this and show your solution.
- 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°.
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
- Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
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.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
- Slope of track
Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitra (167 m AMSL), if the track is 77 km long.
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.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.