# Goniomentry and trigonometry - math word problems

1. Pyramid - angle Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
2. Parallelogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
3. Cuboid Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
4. 4side pyramid Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
5. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
6. n-gon II What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
7. Angle between lines Calculate the angle between these two lines: ? ?
8. Stairway What angle rising stairway if step height in 17 cm and width 27 cm?
9. Climb Road has climbing 1:27. How big is a angle corresponds to this climbing?
10. Goat and circles What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
11. Tetrahedral pyramid Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
12. Angle between vectors Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
13. Jewel Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
14. Rhomboid Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.
15. Slope What is the slope of a line with an inclination 6.06 rad?
16. Steeple Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
17. Pyramid Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
18. n-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
19. Glass At the glass shop we have to cut 8 sheets of glass. Each was shaped a square with sides of 18 cm. We paid 44 CZK. How much is a 1 m2 of glass?
20. Right triangle Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

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.