Chapter 56, Problem 1AR

Add, subtract, multiply, or divide each of the following exercises as indicated.
a. 37°18' + 86°23'
b. 38°46' + 23°43'
c. 136°36'28" - 94°17'15"
d. 58°14' - 44°58'
e. 4(27°23')
f. 3(7°23'43")
g. 87° ÷ 2
h. 103°20' ÷ 4

To determine

(a)

The sum of the given angles.

Answer to Problem 1AR

  ${123}^{°}41^{\prime }$

Explanation of Solution

The sum of the angles is

  ${37}^{°}18^{\prime }+{86}^{°}23^{\prime }={123}^{°}41^{\prime }$

Conclusion:

The sum of angles is ${123}^{°}41^{\prime }.$

To determine

(b)

The sum of the given angles.

Answer to Problem 1AR

  ${62}^{°}29^{\prime }$

Explanation of Solution

The sum of the angles is

  ${38}^{°}46^{\prime }+{23}^{°}43^{\prime }={61}^{°}89^{\prime }$

Since $1^{°}=60^{\prime }$

Then, $89^{\prime }=1^{°}+29^{\prime }$

Thus, ${61}^{°}+1^{°}29^{\prime }={62}^{°}29^{\prime }$

Conclusion:

The sum of angles is ${62}^{°}29^{\prime }.$

To determine

(C)

To subtract the given angles.

Answer to Problem 1AR

  ${42}^{°}19^{\prime }13^{″}$

Explanation of Solution

Subtract ${94}^{°}17^{\prime }15^{″}$ from ${136}^{°}36^{\prime }28^{″}$

Then, ${136}^{°}36^{\prime }28^{″}-{94}^{°}17^{\prime }15^{″}={42}^{°}19^{\prime }13^{″}$

Conclusion:

Therefore, the subtraction of angles is ${42}^{°}19^{\prime }13^{″}$

To determine

(d)

To subtract the given angles.

Answer to Problem 1AR

  ${13}^{°}16^{\prime }$

Explanation of Solution

Subtract ${44}^{°}58^{\prime }$ from ${58}^{°}14^{\prime }$

Then,

  $\begin{array}{l}{58}^{°}14^{\prime }-{44}^{°}58^{\prime }or,\\ {57}^{°}74^{\prime }-{44}^{°}58^{\prime }\left[\therefore 1^{°}=60^{\prime }\right]\\ \Rightarrow {13}^{°}16^{\prime }\end{array}$

Conclusion:

Therefore, the subtraction of angles is ${13}^{°}16^{\prime }.$

To determine

(e)

The product of the given angles.

Answer to Problem 1AR

  ${109}^{°}32^{\prime }.$

Explanation of Solution

Multiply 4 with ${27}^{°}23^{\prime }$

Then, $4\times {27}^{°}23^{\prime }={108}^{°}92^{\prime }$

Since $1^{°}=60^{\prime }$

Then, $92^{\prime }=1^{°}+32^{\prime }$

Thus, ${108}^{°}+1^{°}+32^{\prime }={109}^{°}32^{\prime }$

Conclusion:

Therefore, the product of angles is ${109}^{°}32^{\prime }.$

To determine

(f)

The product of the given angles.

Answer to Problem 1AR

  ${22}^{°}11^{\prime }{9}^{″}.$

Explanation of Solution

Multiply 3 with $7^{°}23^{\prime }43^{″}$

Then,

  $\begin{array}{l}3\times 7^{°}23^{\prime }43^{″}={21}^{°}69^{\prime }129^{″}\\ {21}^{°}+69^{\prime }+120^{″}+9^{″}\left[\therefore 1^{°}=60^{\prime }and{1}^{\prime }=60^{″}\right]\\ \Rightarrow {21}^{°}71^{\prime }{9}^{″}or,\\ \Rightarrow {22}^{°}11^{\prime }{9}^{″}\end{array}$

Conclusion:

Therefore, the product of angles is ${22}^{°}11^{\prime }{9}^{″}.$

To determine

(g)

To divide the given angles.

Answer to Problem 1AR

  ${43}^{°}30^{\prime }$

Explanation of Solution

Divide 87° by 2

Then,

  $\begin{array}{l}2\begin{array}{c}\hfill {43}^{°}\\ \hfill \overline{){87}^{°}}\end{array}\\ \underset{\_}{{86}^{°}}\\ 1^{°}\end{array}$

Now, divide the remainder $1^{°}=60^{\prime }$ again by 2.

  $\begin{array}{l}2\begin{array}{c}\hfill 30^{\prime }\\ \hfill \overline{)60^{\prime }}\end{array}\\ \underset{\_}{60^{\prime }}\\ 0\end{array}$

Combine both the quotient we get

Then, ${43}^{°}+30^{\prime }={43}^{°}30^{\prime }$

Conclusion:

Therefore, the division of angles is ${43}^{°}30^{\prime }.$

To determine

(h)

To divide the given angles.

Answer to Problem 1AR

  ${25}^{°}50^{\prime }.$

Explanation of Solution

Divide 103° by 4

Then,

  $\begin{array}{l}4\begin{array}{c}\hfill {25}^{°}\\ \hfill \overline{){103}^{°}}\end{array}\\ \underset{\_}{{100}^{°}}\\ 3^{°}\end{array}$

Now, divide the remainder $3^{°}=180^{\prime }+20^{\prime }=200^{\prime }$ again by 4.

  $\begin{array}{l}4\begin{array}{c}\hfill 50^{\prime }\\ \hfill \overline{)200^{\prime }}\end{array}\\ \underset{\_}{200^{\prime }}\\ 0\end{array}$

Combine both the quotient we get

Then, ${25}^{°}+50^{\prime }={25}^{°}50^{\prime }$

Conclusion:

Therefore, the division of angles is ${25}^{°}50^{\prime }.$