Goniomentry and trigonometry - examples - page 7
- 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?
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 =.
- 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.
- 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?
- 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°.
- 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.
- The angle of lines
Calculate the angle of two lines y=x-21 and y=-2x+14
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.
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?
A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
Is true equality? ?
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
- Cable car
Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
- Shadow and light
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?
- Inclined plane
On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane.
- Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
- Bearing - navigation
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
- Church tower
Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
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.