Arctangent - practice problems
The arctangent is the inverse function of the tangent function. It is usually denoted arctan z or arctg z; in the English literature, ATAN(z) or tan-1 z is also used. There is also a function atan2 with two arguments, y and x atan2(y,x) = arctg y/x, just that it is also defined for x=0 and in all quadrants of the resulting angle.Instructions: Solve each problem carefully and provide a detailed solution for every item.
Number of problems found: 92
- Angle of elevation 3
The angle of elevation of a pole from a point on the horizontal ground is 15°. After going up a distance of 10m towards the pole the angle of elevation became 30°.What is the height of the pole? - Angle of inclination
Find the angle of inclination of a ramp that rise for 80 cm and is 200 cm long. - The angle 9
The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 m towards the foot of the tower to a point B, the angle of elevation increases to 60°. Find the height of the tower and the distance of the tower - Angle and slope
Find the angle between the x-axis and the line joining the points (3, -1) and (4,-2) . - A boy 5
A boy starts at A and walks 3km east to B. He then walks 4km north to C. Find the bearing of C from A. - Subtract polar forms
Solve the following 5.2∠58° - 1.6∠-40° and give answer in polar form - Cplx sixth power
Let z = 2 - sqrt(3i). Find z6 and express your answer in rectangular form. if z = 2 - 2sqrt(3 i) then r = |z| = sqrt(2 ^ 2 + (- 2sqrt(3)) ^ 2) = sqrt(16) = 4 and theta = tan -2√3/2=-π/3 - View angle
From a tower 20 m high and 20 m away from the river, the width of the river appears to be at an angle of 15°. How wide is the river at this location? - How big is 4
How big is the angle when one side is 20m and the other is 1.5m in a right triangle? - The ladder and wall
A 6.5-meter-long ladder rests against a vertical wall. Its lower end rests on the ground 1.6 meters from the wall. Determine how high the top of the ladder reaches and at what angle it rests against the wall. - Road gradient angle
On the traffic sign that informs about the road's gradient, the figure is 6.7%. Determine the slope angle of the path. What height difference is covered by the car that traveled 2.8 km on this road? - Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - Tram - safe downhill
What is the maximum angle at which the tram can go downhill to still be able to stop? The coefficient of shear friction is f =0.15. - Trapezoid interior angles
Given is an isosceles trapezoid ABCD with bases 10 cm and 14 cm. The height of the trapezoid is 6 cm. Determine the interior angles of the trapezoid. - Triangle tangent area
The tangent of the angle formed by the adjacent sides of the triangle ABC (side a=29 m, b = 40 m) equals 1.05. Calculate the area of that triangle. - Elevation of the tower
We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39°25''. If we come towards its foot 50m closer to place B, we can see the top of the tower from it at an elevation angle of 56°42''. How tall is the tower - Tower elevation angles Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters.
- In the desert
A man wondering in the desert walks 5.7 miles in the direction S 26° W. He then turns 90° and walks 9 miles in the direction N 49° W. At that time, how far is he from his starting point, and what is his bearing from his starting point? - Crosswind
A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed? - Dipole - complex power
For a dipole, calculate the complex apparent power S and the instantaneous value of the current i(t), given: R=10 Ω, C=100uF, f=50 Hz, u(t)= square root of 2 * sin( ωt - 30°). Thanks for any help or advice.
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