# Goniomentry and trigonometry - math word problems

1. Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
2. Hot air balloon
The center of the balloon is at an altitude of 600 m above the ground (AGL). From habitat on earth is the center of the balloon to see in elevation angle 38°20' and the balloon is seen from the perspective of angle 1°16'. Calculate the diameter of the ba
3. Pumps
Five pumps pumped 1,800 hl of water for 3 hours. How many hectoliters of water pump same two powerful pumps for six hours?
4. Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
5. Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
6. Forces
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
7. Bearing
A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
8. Dried apples
How many kilograms of fresh apples id needed to 120 kg of dried apples when from 0.4 tons of fresh apples we get 75 kg of dried apples?
9. Bicycle gears
The toothed wheel on the bicycle pedal has 40 teeth, the wheel on the rear wheel has only 16 teeth. How many times does the rear wheel turn if the pedals rotate 50 times?
10. Gasoline
For nearly full tank of 40 liters of gasoline chauffeur paid 54 euros. How many euros it will cost to go 250 km long if the car has an average fuel consumption 7 liters per 100 kilometers?
11. Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
12. Rails
18 m railway weighs 1260 kg. How much weighs 100 m of welded railways?
13. Glass
How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
14. Cablecar
Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb.
15. Painting rooms
If Dano paint three hours daily given work he complete in 7.5 days. How many hours a day would have to work to finish the job 1.5 days earlier?
16. Right triangle
It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
17. Bonbons
Create a mixture of 50 kg of candy on price 700Kč. Candies has prices: 820Kč, 660Kč and 580Kč. Use cross rule.
18. Diver and pressure
Determine what pressures is exposed diver without a suit at a depth of 15 meters, with a small space suit at a depth of 25 meters and a massive suit at a depth of 70 m in water.
19. Sugar
From 3 tons of sugar beet was produced 480 kg of sugar. How many tons of sugar was produced from 17.5 tons of sugar beet?
20. Good swimmer
Good swimmer swims 23 m distance with ten shots. With how many shots he swim to an island located 81 m if still swims at the same speed?

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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.