Question

(5 degree 37 minute 30 second) change it into radian measures.

Answer 1

Answer:

5 degree 37 minute 30 second=0.098 Radians.

Explanation:

5°37'30"

First change the whole expression into the degree.

We know that the 1 minute=60 seconds.

So,30 second = 0.5 minutes.

1 degree=60 minutes

So, 37.5 minutes =0.625 degree

5°37'30"=5°+0.625°=5.625°

We know that the

$\pi$Radians=180°

$1\ Degree=\dfrac{\pi }{180}\ Radians$....................(1)

So,multiply equation (1) both sides by 5.625

we get,

$5.625\ Degree=\dfrac{\pi\times 5.625 }{180}\ Radians$

$5.625\ Degree=0.098 Radians$

So,

5 degree 37 minute 30 second=0.098 Radians.

Answer 2

Given:

Angles in degrees $=5^{o}$ $37'$ $30''$

To find:

The value of angles in radians.

Solution:

We have been given the value of angles in degrees and we know, to change an angle $x^{o}$ to $x$ $rad$ is,

$x$ $rad=x^{o}$ × $\frac{\pi }{180}$

Also, we have,

$1^{o} =60'$

$1'=60''$

Step 1

To convert 30 seconds into degrees, we divide the value by 3600 seconds.

We get,

$x^{o}=5^{o}37'\frac{30}{3600}$

Also, to convert 37 minutes to degrees, we divide 37 min by 60.

$x^{o}=5^{o}+(\frac{37}{60} )^{o} +(\frac{30}{3600} ) ^{o}$

$x^{o}=5^{o}+ (0.61667)^{o}+ (0.00834)^{o}$

$x^{o} =5.625^{o}$

Step 2

Now,

The value of this angle in radians will be

$x$ $rad=5.625$ × $\frac{\pi }{180}$

$x$ $rad=5.625$ × $\frac{1}{180}$ × $\frac{22}{7}$

$x$ $rad=0.03125$ × $\frac{22}{7}$

$x$ $rad=0.098125^{o}$

Final answer:

Hence, the value of the given angles in degrees to radians is 0.098125 radians.