# Two forces

The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.

Correct result:

F =  1053.418 N

#### Solution:

$F_{1}=580 \ \text{N} \ \\ F_{2}=630 \ \text{N} \ \\ A=0 \ ^\circ \ \\ B=59 \ ^\circ \ \\ \ \\ x=F_{1} \cdot \ \cos A ^\circ + F_{2} \cdot \ \cos B ^\circ =F_{1} \cdot \ \cos 0^\circ \ + F_{2} \cdot \ \cos 0^\circ \ =580 \cdot \ \cos 0^\circ \ + 630 \cdot \ \cos 0^\circ \ =580 \cdot \ 1 + 630 \cdot \ 1=904.47399 \ \\ y=F_{1} \cdot \ \sin A ^\circ + F_{2} \cdot \ \sin B ^\circ =F_{1} \cdot \ \sin 0^\circ \ + F_{2} \cdot \ \sin 0^\circ \ =580 \cdot \ \sin 0^\circ \ + 630 \cdot \ \sin 0^\circ \ =580 \cdot \ 0 + 630 \cdot \ 0=540.0154 \ \\ F=\sqrt{ x^2+y^2 }=\sqrt{ 904.474^2+540.0154^2 }=1053.418 \ \text{N}$

Try calculation via our triangle calculator.

We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!

Showing 1 comment:

Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Median
In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
• The right triangle
In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
• Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the length of the arm is 17 cm and the height to the base is 12 cm.
• RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
• Vertices of RT
Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
• Cable car 2
Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
• Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
• Flowerbed
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?
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
• Circle - AG
Find the coordinates of circle and its diameter if its equation is: ?
• A truck
A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
• Vector - basic operations
There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w
• Sines
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
• Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)