# Goniomentry and trigonometry - math word problems

1. 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?
2. 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.
3. Two forces
The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
4. Clouds
Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
5. Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
6. Driver
I drive at an average speed of 70km/h, I drive 10 thousand km. How long did it take me?
What is the slope of a ladder 6.2 m long and 5.12 m in height.
8. Sugar 9
150 kg of sugar beet yields 24 kg of sugar. From how many tons of sugar beet can be obtained three tons of sugar?
9. The mast
A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
10. ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
11. Perimeter of triangle
In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
12. Two boats
The sightseeing boat sail at 25 km / h. The cruise take 6 hours. How long the another boat sails at 60 km/h?
A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ?
14. Inner angles
The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
15. A map
A map of size 60cm by 25cm is reduced in the ratio of 3:5, twice. What are the new dimensions?
16. Water channel
The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo
17. Crown coins
Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?
18. 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.
19. Parallelogram +ľ
| AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram.
20. 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.

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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.