# Arctangent + Pythagorean theorem - examples

1. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
2. River
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
3. Cube - angles
Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
4. 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.
5. V-belt
Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
6. Goniometric form
Determine goniometric form of a complex number ?.
7. Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°

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Pythagorean theorem is the base for the right triangle calculator.