Question

Find the degree measure of the angle with the given radian measure.

$3.4$

Short answer

$\mathbf{194}\mathbf{.}{\mathbf{91}}^{\mathbf{\circ }}$

Step-by-step solution

Step 1. Given information.

The given radian measure is:

3.4 rad.

Step 2. Explanation.

We know that

$1\text{\hspace{0.17em}radian\hspace{0.17em}=\hspace{0.17em}}\left(\frac{{180}^{\circ }}{\pi }\right)$

Thus to find the degrees of the angle multiply the radian measure with$\left(\frac{{180}^{\circ }}{\pi }\right)$

Here the radian measure $\pi$is not available so when we multiply put$\pi =3.14$.

Step 3. Calculation.

To convert radians to degrees, multiply by:$\left(\frac{{180}^{\circ }}{\pi }\right)$

$\text{3.4rad}=\left(3.4\text{\hspace{0.17em}x\hspace{0.17em}}\frac{180}{\pi }\right)$

Put$\pi =3.14$ in the expression, we get:

$\begin{array}{l}={\left(3.4x\frac{180}{3.14}\right)}^{{}^{\circ }}\\ ={\left(\frac{612}{3.14}\right)}^{\circ }\\ ={194.91}^{\circ }\end{array}$