# Goniomentry and trigonometry - math word problems

1. Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
2. Building
How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
3. Equilateral triangle
How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
4. River
From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
5. Triangle in circle
Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
6. Slope
What is the slope of a line with an inclination 6.06 rad?
7. IS triangle
Calculate interior angles of the isosceles triangle with base 46 cm and legs 49 cm long.
8. Rhombus
Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
9. Angles
Determine the interior angles of a rhombus with area 319.1 cm2 and perimeter 72 cm.
10. Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
11. Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
12. Rhomboid
Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°.
13. Cotangent
If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
14. 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.
15. Triangle TBC
TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
16. Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
17. Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
18. Forces
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.
19. Climb
Road has climbing 1:27. How big is a angle corresponds to this climbing?
20. Pentagon
Calculate the area of regular pentagon, which diagonal is u=17.

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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.