To determine the measure of an angle given the tangent value, follow these steps:
1. Understand the given information: We are given the tangent of an angle, which is 0.8. The tangent function relates the angle to the ratio of the opposite side to the adjacent side in a right triangle.
2. Find the angle using arctangent: To find the angle whose tangent is 0.8, we need to use the arctangent function.
3. Convert the angle to degrees: Arctangent will initially provide the angle in radians. We must convert this value from radians to degrees because standard angle measures are typically given in degrees.
4. Round to the nearest tenth: The final step is to round the calculated angle to the nearest tenth of a degree.
With these steps carefully followed, we find that the angle whose tangent is 0.8 is:
1. The tangent value is 0.8.
2. Calculate the angle in radians using the arctangent function.
3. Convert the calculated angle from radians to degrees.
4. Round the resulting angle to the nearest tenth.
The correct measure of the angle, when rounded to the nearest tenth, is:
38.7°
Hence, out of the given options (53.1°, 56.7°, 82.9°, 38.7°), the correct choice is:
38.7°
