To calculate 83 / sin(38 degrees), we first need to find the sine of 38 degrees. The sine of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. However, for most calculations, especially those involving specific degree measures like 38 degrees, we use a calculator or a trigonometric table to find the sine value.
Step-by-Step Calculation
Here’s how you can do it step by step:
Find the Sine of 38 Degrees
Using a calculator, set it to degrees mode and input sin(38). The result should be approximately 0.6157. This value represents the sine of 38 degrees.
Divide 83 by the Sine of 38 Degrees
Now, divide 83 by the sine of 38 degrees, which we found to be approximately 0.6157. So, the calculation is 83 / 0.6157.
The result of this division is approximately 134.73. Therefore, 83 / sin(38 degrees) is approximately 134.73.
| Operation | Value |
|---|---|
| Sin(38 degrees) | 0.6157 |
| 83 / Sin(38 degrees) | 134.73 |
This calculation can be useful in various mathematical and real-world applications, such as physics, engineering, and geometry, where trigonometric ratios are used to solve problems involving right-angled triangles.
What is the sine function used for?
+The sine function is used to find the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right-angled triangle. It has numerous applications in mathematics, physics, engineering, and other fields.
How do I calculate the sine of an angle without a calculator?
+Without a calculator, you can use trigonometric tables or approximations based on known values of sine for certain angles. However, for precise calculations, especially with non-standard angles, a calculator or computer software is recommended.
