True thickness is measured using trigonometric principles, particularly when the apparent thickness is viewed at an angle. The process involves using the apparent thickness (measured along a slanted plane), the angle of the slope, and the appropriate trigonometric function to calculate the perpendicular or true thickness.
Here's how it's done, referencing the information from the YouTube video provided:
Calculating True Thickness
The video discusses finding an adjacent side (true thickness) when you have the hypotenuse (apparent thickness) and the angle:
- Understanding the Scenario: You are trying to determine the vertical, or true thickness of a layer, but what you have is a thickness measurement taken along a slope (the hypotenuse).
- The Key: We use the cosine function (cos) in trigonometry.
- Formula:
Adjacent = Hypotenuse * cos(angle)- Adjacent: This is the true thickness – what we want to calculate.
- Hypotenuse: This is the apparent thickness – the measurement along the slope.
- Angle: This is the angle of the slope in relation to the horizontal (or the angle between the true thickness and the apparent thickness).
- Application:
- If you know the apparent thickness (the measurement along a slope) and the angle of that slope, you can calculate the true thickness by multiplying the apparent thickness by the cosine of the angle.
- For instance, if the apparent thickness (hypotenuse) is 10 cm and the angle is 30 degrees, you would perform:
True Thickness = 10 cm * cos(30°). Since cos(30°) is about 0.866, true thickness would be approximately10 * 0.866 = 8.66 cm.
- For instance, if the apparent thickness (hypotenuse) is 10 cm and the angle is 30 degrees, you would perform:
- If you know the apparent thickness (the measurement along a slope) and the angle of that slope, you can calculate the true thickness by multiplying the apparent thickness by the cosine of the angle.
Example of Calculation
| Measurement | Value |
|---|---|
| Apparent Thickness | 10 cm |
| Slope Angle | 30 degrees |
| Cos(30 degrees) | ~0.866 |
| True Thickness | ~8.66 cm |
Practical Insights
- Accuracy: Accurate angle measurement is key to obtaining a precise true thickness value.
- Real-World: This technique is used in geology (measuring tilted rock layers) and engineering (measuring thickness across an incline), where direct measurements aren't easily available.
Summary
By using the apparent thickness and the slope angle, you can calculate the true thickness by applying basic trigonometric principles and the cosine formula.
