Chapter 1, Problem 3RP

a.

To determine

The sum of two given angles

Answer to Problem 3RP

The sum of the two given angles will be $35°4^{\prime }69^{″}$

Explanation of Solution

Given information:

Angle 1: $43°15^{\prime }17^{″}$

Angle 2: $25°49^{\prime }18^{″}$

First of all, we will add seconds:

  $17^{″}+18^{″}=35^{″}$

Now, add minutes:

  $15^{\prime }+49^{\prime }=64^{\prime }$

Since, $64^{\prime }>60$ ',

  $64^{\prime }-60^{\prime }=4^{\prime }$ and $60^{\prime }\left(=1°\right)$ will be carried forward (added) to degrees

Add degrees with carry-over from minutes: $1°+43°+25°=69°$

Hence,

  $43°15^{\prime }17^{″}+25°49^{\prime }18^{″}=69°04^{\prime }35^{″}$

b.

To determine

The difference of two given angles

Answer to Problem 3RP

The difference of two given angles will be $50°59^{\prime }43^{″}$

Explanation of Solution

Given information:

Angle 1: $90°$ and

Angle 2: $39°17^{″}$

First, convert $90°$ in minutes and seconds.

We can write,

  $90°=89°59^{\prime }60^{″}$

Now, let us subtract seconds

  $60^{″}-17^{″}=43^{″}$

Now, we will subtract minutes

  $59^{\prime }-0^{\prime }=59^{\prime }$

And then, subtract degrees

  $89°-39°=50°$

Hence,

  $89°59^{\prime }60^{″}-39°00^{\prime }17^{″}=50°59^{\prime }43^{″}$