Question

Convert the following angle into radian: \[{65^ \circ }30'\].

Answer 1

Hint: Here we need to solve by using conversion method, here we need to understand that for converting degree into radian we need to divide by three hundred sixty degree, and when comes to minute here we need to first convert minute into degree then degree into radians.

Formula used:
To convert the degree into the radians we need to solve by:
\[ \Rightarrow radian = \dfrac{\pi }{{180}}(\deg ree)\]
To convert the minute into degree we need to solve by:
\[ \Rightarrow \deg ree = \dfrac{{\min ute}}{{60}}\]

Complete answer:
Here to solve for the given question, we need to solve by the conversion method:
Here we see that we are given with degree and minute value both, so first minute value will be converted to degree, and then when the complete term will be converted into degree then the term will be converted to radian.
\[ \Rightarrow {65^ \circ }30' = \left[ {\left( {\dfrac{\pi }{{180}} \times 65} \right) + \left( {\dfrac{\pi }{{180}} \times \left[ {\dfrac{{30}}{{60}}} \right]} \right)} \right] = \left[ {0.36 \times 3.14 + 0.002 \times 3.14} \right] = (1.1304 + 0.00872) = 1.13912\]
Here we get the answer after conversion into radian.

Note:
Here we solve the given question by using the conversion method, by solving with the relation we know between the minutes, degree and radian. And to solve this question here we need to recall the values associated with the relationship, otherwise there is a method to convert the given quantities from one to another.