# Goniomentry and trigonometry - math word problems

- 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? - Tree shadow 3

A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ? - 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? - Loading car

The car was loaded with 78 boxes weighing 19 kg. How many 25kg boxes can load if the total weight is the same? - Cone

The rotating cone volume is 9.42 cm^{3}, with a height 10 cm. What angle is between the side of the cone and its base? - 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? - 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 - 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. - 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? - 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? - Road drop

On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane? - 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? - 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? - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6 - 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 - 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? - Drying apples

By drying, apples lose 85% of their weight. How many kgs of dried apples do we get from 820 kilograms of fresh? - 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° - 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. - 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.