# Goniomentry and trigonometry - examples - page 10

1. 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.
2. Johnny Johnny bought for 28 CZK flower to mum. He that spent 4/7 of the money saved. How much money he had saved? How much money left him?
3. Scalar dot product Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
4. 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.
5. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
6. V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
7. 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?
8. Ladder slope What is the slope of a ladder 6.2 m long and 5.12 m in height.
9. 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?
10. Pentagon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
11. 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 flow
12. Rails 18 m railway weighs 1260 kg. How much weighs 100 m of welded railways?
13. Driver The driver of the supply car reckoned that at the average speed of 72 km/h arrives to the warehouse for 1 1/4 hours. After 30 km however unintentionally drove to the gas station and have ten minutes delay. At what average speed would have to go the rest.
14. Cablecar Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb.
15. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
16. Collecting For the first week of material collection events are picked up at the school 850 kg of paper and 305 kg of rags which represented 55% of total collection for 14 days. How many kilograms of secondary raw materials were handed over totally?
17. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
18. 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?
19. 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?
20. Tree Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?

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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.