# Goniomentry and trigonometry - math word problems

1. Diagonal Diagonal of the rectangle has length 46.4 cm. Angle between diagonal and londer sife of rectangle is 22°. Calculate area of the rectangle.
2. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
3. Cone Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
4. Tower How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
5. Gon functions Decide which of the numbers (values ​​of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1.
6. Triangle Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
7. Greatest angle Calculate the greatest triangle angle with sides 197, 208, 299.
8. Q-Exam If tg α = 0.9, Calculating sin α, cos α, cotg α . Average climb of the road is given by ratio 1:15. By what angle road average climb?
10. Triangle Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
11. SAS triangle The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
12. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
13. Climb On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
14. Aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
15. Reflector Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
16. Parallelogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
17. Side c In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
18. Two boats Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.
19. Stairway What angle rising stairway if step height in 17 cm and width 27 cm?
20. Observer The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from the another end of the fence?

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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.