Question

How do you convert the angle $ - {135^ \circ }36''$ in decimal degree form?

Answer 1

Hint: In this question, we are going to convert the given angle to decimal degree form.
The given angle contains degree and seconds.
In this we are going to use the decimal degree formula.
We are going to convert that angle into the decimal degree form by adding the degree, minutes and seconds.

Formula used: To calculate decimal degrees, we use the DMS to decimal degree formula below;
Decimal degrees = degrees+ $\left( {\dfrac{{Minutes}}{{60}}} \right)$ + $\left( {\dfrac{{\sec ond}}{{3600}}} \right)$

Complete step-by-step solution:
In this question, we are going to convert the given angle to decimal degree form.
First write the given angle and mark it as$\left( 1 \right)$.
$ - {135^ \circ }36''...\left( 1 \right)$
Here in the given angle, $ - 135$ represent the degree and $36$represent the seconds.
Now we are going to convert the given angle into the decimal degree form:
The given angle contains degree and seconds, it does not contain minutes.
So put minutes equal to zero.
Now we are going to use the Decimal degree formula
DD=d+ (min/60) + (sec/60)
$ \Rightarrow - {135^ \circ } + \dfrac{0}{{60}} + \dfrac{{36}}{{3600}}$
Dividing the above term we get,
$ \Rightarrow - {135^ \circ } + 0 + 0.01$
Add up the integer number of degrees and seconds, we get
$ \Rightarrow - {135^ \circ } + 0.01$
$ \Rightarrow - {134.99^ \circ }$

Thus we get the converted degree for the angle $ - {135^ \circ }36''$ is $ - {134.99^ \circ }$

Note: Add up the integer number of degrees and minute/second fractions to convert the angle magnitude into the decimal form.
Decimal degree express latitude and longitude geographic coordinates as decimal fractions of a degree
One minute is equal to sixty seconds.
One degree is equal to one hour that is equal to sixty minutes or three thousand hundred seconds.