Using trigonometry A patients leg is raised at an angle of 45 degrees and a traction force of 50N is applied in line with the leg; Find the vertical component of this force? Find the horizontal component of this force?
vertical= 50sin45
horizontal= 50cos45
To find the vertical and horizontal components of the force applied on the patient's leg, we can use trigonometric functions.
Let's start by labeling the given information:
Angle between the leg and the force = 45 degrees
Traction force applied = 50N
To find the vertical component of the force, we can use the sine function. The vertical component will be the force acting in the upward direction.
Vertical component of the force = Traction force * sin(angle)
Vertical component of the force = 50N * sin(45°)
Now, we need to find the value of sin(45°). Using the reference angles for sine, we know that sin(45°) = sin(90° - 45°) = sin(45°). So, we can simply use the value of sin(45°) as 0.7071.
Vertical component of the force = 50N * 0.7071
Vertical component of the force = 35.355N (approximately)
Therefore, the vertical component of the force applied to the leg is approximately 35.355N.
Next, let's find the horizontal component of the force. The horizontal component will be the force acting in the sideways direction.
Horizontal component of the force = Traction force * cos(angle)
Horizontal component of the force = 50N * cos(45°)
Similar to above, we need to find the value of cos(45°). Using the reference angles for cosine, we know that cos(45°) = cos(90° - 45°) = sin(45°). Again, we can use the value of cos(45°) as 0.7071.
Horizontal component of the force = 50N * 0.7071
Horizontal component of the force = 35.355N (approximately)
Therefore, the horizontal component of the force applied to the leg is approximately 35.355N.
In summary, the vertical component of the force is approximately 35.355N and the horizontal component of the force is also approximately 35.355N.