# Goniomentry and trigonometry - math word problems

1. 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? A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ?
3. 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? The car was loaded with 78 boxes weighing 19 kg. How many 25kg boxes can load if the total weight is the same?
5. Cone The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
6. 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?
7. 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 bal
8. 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.
9. Regular n-gon Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
10. Candies There are red, blue and green candies in bad. Red to green is in 6:11 ratio and blue to red in a 7: 5 ratio. In what proportion are blue to green candies? On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
12. Medians of isosceles triangle The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
13. 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?
14. Scalene triangle Solve the triangle: A = 50°, b = 13, c = 6
15. Find the area Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft
16. 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?
17. Drying apples By drying, apples lose 85% of their weight. How many kgs of dried apples do we get from 820 kilograms of fresh?
18. 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°
19. 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.
20. Driver I drive at an average speed of 70km/h, I drive 10 thousand km. How long did it take me?

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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.