Did I Solve the Vertical Post Problem Correctly Using SOH CAH TOA?

In summary, the vertical post in the given image is held upright by two tensional cables. The horizontal components of the tensions balance each other, while the vertical components do not need to be equal as they are balanced by the force from the ground. The correct angle for Theta is 63 degrees, which can be calculated using the formula SOH CAH TOA. This explains why 33 degrees is not the correct angle for Theta.
  • #1
Ryan Lau
13
0

Homework Statement


A vertical post is held in place by two cables as shown.

Homework Equations


SOH CAH TOA

The Attempt at a Solution


http://postimg.org/image/6rgssb1j5/

The answer in the textbook is 63 degrees. Is this an issue or did I do something terribly wrong?
 
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  • #2
The tension in the cables keep the post in vertical position. Its top point can not move sideways, the horizontal components of the tensions balance each other.
The vertical components do not need to be equal, as they are balanced by the force from the ground.
 
  • #3
ehild said:
The tension in the cables keep the post in vertical position. Its top point can not move sideways, the horizontal components of the tensions balance each other.
The vertical components do not need to be equal, as they are balanced by the force from the ground.
Unfortunately, I do not fully comprehend this explanation. My question is why 33 degrees is not the correct angle for Theta.
 
  • #4
Ryan Lau said:
Unfortunately, I do not fully comprehend this explanation. My question is why 33 degrees is not the correct angle for Theta.
You calculated theta from the condition that the vertical components of the tensions are equal, which is wrong .
 
  • #5
ehild said:
You calculated theta from the condition that the vertical components of the tensions are equal, which is wrong .

I believe I understand this comment now.

Overview:
To keep the vertical post upright, both the left and right side of the ground by the tensional strings will be equal to each other.

1500cos50 = 964.1814 N = Adjacent Side (floor)
Cos Inv. (964.1814/2100) = 62.6688 N (angle required to keep the pole upright)
 
  • #6
And the rounded value is 63°.
 

1. What are angles and how are they measured?

Angles are geometric figures formed by two rays or lines meeting at a point. They are typically measured in degrees, with a full circle being 360 degrees.

2. How do you calculate the measure of an angle?

The measure of an angle can be calculated using the formula: angle = arc length / radius. This formula applies to all types of angles, including acute, right, and obtuse angles.

3. What are the different types of angles?

There are four types of angles: acute, right, obtuse, and straight. Acute angles measure less than 90 degrees, right angles measure exactly 90 degrees, obtuse angles measure between 90 and 180 degrees, and straight angles measure exactly 180 degrees.

4. How do you use the Pythagorean Theorem to calculate angles?

The Pythagorean Theorem states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem can be used to calculate angles in a right triangle by finding the inverse trigonometric function of the sides.

5. How do you use trigonometric functions to calculate angles?

Trigonometric functions, such as sine, cosine, and tangent, can be used to calculate angles in a right triangle. These functions involve using the ratios of the sides of the triangle to find the measure of the angle. For example, the sine function is equal to the opposite side divided by the hypotenuse.

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