Question

2.82 convert the following radian measure to degrees. 2.82 radians = (round to the nearest minute as needed.)

Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we use the formula $D = R\times\frac{180^{\circ}}{\pi}$, where $D$ is the measure in degrees and $R$ is the measure in radians.

Step2: Substitute the given value

Substitute $R = 2.82$ into the formula: $D=2.82\times\frac{180^{\circ}}{\pi}$.

Step3: Calculate the value in degrees

$D=\frac{2.82\times180}{\pi}\approx\frac{507.6}{\pi}\approx 161.6^{\circ}$.

Step4: Convert the decimal part to minutes

The decimal part is $0.6^{\circ}$. Since $1^{\circ}=60'$, then $0.6\times60 = 36'$.

Answer:

$161^{\circ}36'$