# Goniomentry and trigonometry - math word problems

1. Cuboid 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).
2. Goat and circles What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which
3. Building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
4. Tree How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
5. Angle A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
6. Sinus Determine the smallest integer p for which the equation 4 sin x = p has no solution.
7. Pentagonal pyramid Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
8. Triangular prism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
9. Hexagon 5 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
10. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
11. Vector sum The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
12. Diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
13. Cosine Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
14. ISO trapezium Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
15. 30-60-90 The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
16. Angle between vectors Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
17. Chord - TS The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
18. EQL triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
19. Flowerbed Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
20. Cable car 2 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?

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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.