Questions: Convert the following angle in radians to degrees. 2.96 2.96 radians ≈ ◻ ∇° (Type an integer or decimal rounded to two decimal places as needed.)

Transcript text: Convert the following angle in radians to degrees. \[ 2.96 \] 2.96 radians $\approx$ $\square$ $\nabla^{\circ}$ (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Solution Steps

To convert an angle from radians to degrees, we use the formula: \[ \text{degrees} = \text{radians} \times \left(\frac{180}{\pi}\right) \] We will use this formula to convert 2.96 radians to degrees and round the result to two decimal places.

Step 1: Given Angle in Radians

We start with the given angle in radians: \[ \text{radians} = 2.96 \]

Step 2: Conversion Factor

The conversion factor from radians to degrees is: \[ \frac{180}{\pi} \approx 57.2958 \]

Step 3: Convert Radians to Degrees

Using the conversion factor, we convert the angle from radians to degrees: \[ \text{degrees} = 2.96 \times 57.2958 \approx 169.5955 \]

Step 4: Round to Two Decimal Places

We round the result to two decimal places: \[ \text{degrees\_rounded} \approx 169.60 \]