Question 1186007: the resultant of two forces acting at right angles to each other is 80 degrees N. If one of the forces is 45 deg N, what is the other force and the angle it makes with resultant
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to solve this problem:
**1. Visualize the forces:**
Imagine the two forces (let's call them F1 and F2) acting at right angles. Their resultant (R) is the vector sum of these forces. We can visualize this as a right triangle, where F1 and F2 are the legs, and R is the hypotenuse.
**2. Use the Pythagorean theorem:**
R² = F1² + F2²
We know R = 80 N and F1 = 45 N. We need to find F2.
80² = 45² + F2²
6400 = 2025 + F2²
F2² = 4375
F2 = √4375 ≈ 66.14 N
**3. Find the angle between the resultant and the known force (F1):**
Let θ be the angle between the resultant (R) and F1. We can use trigonometry:
tan(θ) = F2 / F1
tan(θ) = 66.14 / 45
tan(θ) ≈ 1.47
θ = arctan(1.47) ≈ 55.7°
**4. Find the angle between the resultant and the other force (F2):**
Since the forces are at right angles, the angle between F2 and the resultant will be 90° - θ.
Angle between R and F2 = 90° - 55.7° ≈ 34.3°
**Answers:**
* The other force (F2) is approximately **66.14 N**.
* The angle it makes with the resultant is approximately **34.3°**.
Answer by ikleyn(52852)  (Show Source):
You can put this solution on YOUR website! .
One note and teaching to the person, who created this post
and to the next generation of students, who will read it.
To write "the resultant of two forces acting at right angles to each other is 80 degrees N"
is the highest degree of illiteracy, because degrees are irrelevant to this sentence.
The correct writing is "the resultant of two forces acting at right angles to each other is 80 N".
To write "one of the forces is 45 deg N" (as in the next sentence),
is the same degree of illiteracy, because "deg" are irrelevant to this sentence.
The correct writing is "one of the forces is 45 N".
After these corrections, the problem is ready to be solved.
I suspect, that the problem was accepted via a phone by former English teacher,
who decided to switch his business to the area of Math education
and serves there as a phone dispatcher, but does not understand the meaning of phone messages.
Many posts at this forum are written in the same style.
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