# Goniomentry and trigonometry - examples - page 9

1. Chimney Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney.
2. Perimeter of triangle In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
3. Right triangle trigonometrics Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
4. Crown coins Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?
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. Traffic laws Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
7. Segment in a triangle In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
8. Rhombus One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
9. Four sides of trapezoid In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
10. Two triangles SSA Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
11. High wall I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
12. Triangle Calculate the area of right triangle ΔABC, if one leg is long 14 and its opposite angle is 59°.
13. Painters Five painters painting the fence for eight days. How many days over will take work if paint the fence only four decorators?
14. Bonbons Create a mixture of 50 kg of candy on price 700Kč. Candies has prices: 820Kč, 660Kč and 580Kč. Use cross rule.
15. Angles by cosine law Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
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. Sinus Determine the smallest integer p for which the equation 4 sin x = p has no solution.
18. New computer New computer process a certain amount of data for 6 hours. For how many hours will process the same amount of data older computer that has a quarter lower performance?
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. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)

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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.