# Goniomentry and trigonometry - math word problems

1. An angle
An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
3. Children playground
The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles.
4. Five inlets
The tank can be filled with five equally powerful inlets. If the tank is filled by four of these inlets, it takes a total of 30 minutes to fill one-third of the tank. How many minutes does it take to fill an empty tank if it is filled with all five inlets
5. Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
6. Sugar production
From 1 ton of beet, 150 kg of sugar is produced. To clean 1 ton of sugar 450 kg of lime is consumed. Calculate how many kgs of lime is consumed when processing 1 ton of sugar beet?
7. Calculate 2
Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
8. Substitution method
Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
9. Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?
10. Diagonals of the rhombus
How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?
11. The mast
The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
12. Inlet and outlet
The pool has a capacity of 50 hl. The inlet pipe flows in 1 minute 1.25 hl, and the waste pipe outlet is draining the full pool in 50 minutes. How long will take the empty the full pool when both the inlet and outlet are opened at the same time?
13. Two bricks
One brick weighs 1kg and half a brick, how many weigh two bricks?
14. Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
15. Bicycle gear
The pedal bicycle wheel has 56 teeth and a rear 20 gear tooth. How many times does the bicycle wheel turn when you make 20 turns of the pedal wheel?
16. Apples
School kitchen bought 36kg apples for 12 kc/kg. How many kilograms of apples 1/4 cheaper can they buy for the same money?
17. Proportion 2
A car is able to travel 210 km in 3 hours. How far can it travel in 5 hours? Put what kind of proportion is this and show your solution.
18. Deviation of the lines
Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
19. Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
20. Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m

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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.