# Goniomentry and trigonometry - examples - page 3

1. n-gon II
What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
2. Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
3. Stairway
What angle rising stairway if step height in 17 cm and width 27 cm?
4. Climb
Road has climbing 1:27. How big is a angle corresponds to this climbing?
5. 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
6. Angle between lines
Calculate the angle between these two lines: ? ?
7. 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.
8. Jewel
Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
9. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
10. Slope
What is the slope of a line with an inclination -221°?
11. Rhomboid
Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.
12. 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?
13. 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.
14. n-gon
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
15. 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.
16. Rhombus
Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
17. Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
18. V-belt
Calculate the length of the belt on pulleys with diameters of 113 mm and 308 mm at shaft distance 190 mm.
19. House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?