# Goniomentry and trigonometry - 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? - A boy

A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff. - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Trapezoid - intersection of diagonals

In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area. - Five pumps

The water tank is filled with two pumps in 48 minutes. How long would it take to fill it with 5 same pumps? - 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°. - River

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. - Observer

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? - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Right

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

Triangle KLM is given by plane coordinates of vertices: K[-2, -20] L[4, 1] M[-16, 4]. 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 of the rail tracks between Prievidza (309 m AMSL) and Topoľčany (174 m AMSL), if the track is 44 km long. - Pentagon

Calculate the area of regular pentagon, which diagonal is u=19.

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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.