# Goniomentry and trigonometry - examples - page 7

1. Diagonals
Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
2. Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
3. Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
4. Height 2
Calculate the height of the equilateral triangle with side 38.
5. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
6. Building
The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
7. SAS triangle
The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
8. Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
9. Triangle
Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
10. Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
11. Greatest angle
Calculate the greatest triangle angle with sides 197, 208, 299.
12. 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.
13. Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
14. Flowerbed
Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =.
15. 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.
16. Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
17. Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
19. The angle of lines
Calculate the angle of two lines y=x-21 and y=-2x+14
20. Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.

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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.