Chapter 1.2, Problem 11PSA

To determine

To find: The measurement of angle $\angle RAT$ .

Answer to Problem 11PSA

  $\angle RAT={51}^0{53}^{\text{'}}{50}^{\text{'}\text{'}}$ .

Explanation of Solution

Given information:

A figure is given as below. $\angle CAR$ is a right angle and $m\angle CAT={37}^0{66}^{\text{'}}{10}^{\text{'}\text{'}}$

  

Calculation:

A figure is given as below.

  

  $\angle CAR$ is a right angle and $m\angle CAT={37}^0{66}^{\text{'}}{10}^{\text{'}\text{'}}$ .

  $\begin{array}{l}\text{Here, }\angle CAR=\angle CAT+\angle RAT\\ \Rightarrow \angle RAT=\angle CAR-\angle CAT\\ \Rightarrow \angle RAT={90}^0{0}^{\text{'}}{0}^{\text{'}\text{'}}-{37}^0{66}^{\text{'}}{10}^{\text{'}\text{'}}\\ \Rightarrow \angle RAT={90}^0{0}^{\text{'}}{0}^{\text{'}\text{'}}-{38}^0{06}^{\text{'}}{10}^{\text{'}\text{'}}\\ \Rightarrow \angle RAT={51}^0{53}^{\text{'}}{50}^{\text{'}\text{'}}\end{array}$