Goniometry and trigonometry - practice problems
Number of problems found: 344
- A rectangle 5
A rectangle has sides of 10 cm and 14 cm. Calculate the angle between a diagonal and alongside.
- One side
One side is 36 long with a 15° incline. What is the height at the end of that side?
If tg α = 9.6, Calculating sin α, cos α, cotg α .
- Height 2
Calculate the height of the equilateral triangle with side 27.
- Substitution method
Solve goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2
- Isosceles trapezoid
Find the height in an isosceles trapezoid if the area is 520 cm² and the base a = 25 cm and c = 14 cm. Calculate the interior angles of the trapezoid.
- Centre of the hypotenuse
For the interior angles of the triangle ABC, alpha beta and gamma are in a ratio of 1: 2: 3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB.
- Calculate triangle
In the triangle ABC, calculate the sizes of all heights, angles, perimeters and its area, if given a-40cm, b-57cm, c-59cm
- The chimney
How high is the chimney if we see it from a distance of 60 m at an angle of 42°?
- Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm and the angle formed by them is 30 degrees.
- Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
- One of
One of the internal angles of the rhombus is 120° and the shorter diagonal is 3.4 meters long. Find the perimeter of the rhombus.
- The farmer
The farmer sees the back fence of the land, which is 50 m long at a viewing angle of 30 degrees. It is 92 m away from one end of the fence. How far is it from the other end of the fence?
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area?
- The ladder
The ladder touch on a wall at a height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm² (B) 20 cm² (C) 30.78 cm² (D) 31.84 cm² (E) 32.90 cm2
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?
- Two triangles SSA
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
- Altitude angles
Cities A, B, C lie in one elevation plane. C is 50 km east of B, B is north of A. C is deviated by 50° from A. The plane flies around places A, B, C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Find the altit
- Bridge diagonally across the river
The width of the river is 89 m. For terrain reasons, the bridge deviates from a common perpendicular to both banks by an angle of 12° 30 '. Calculate how many meters the bridge is longer than the river.
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.