Chapter 8.5, Problem 11CE

To determine

To determine the correct statements and explain which statement is easier to use.

Answer to Problem 11CE

The correct statement will be $(\text{b}),x\approx 27\times 1.1918,$ and $(\text{c})\text{, }x=\frac{27}{0.8391}$ .

Explanation of Solution

Given:

Two ways to find the value of $x$ are started below:

Way − 1, that is,

using $\tan 40°,$

  $\Rightarrow \tan {40}^0=\frac{27}{x}$,$\Rightarrow 0.8391\approx \frac{27}{x}$.

Way − 2, that is,

using $\tan 50°,$

  $\Rightarrow \tan {50}^0=\frac{x}{27}$ ,

  $\Rightarrow 1.1918\approx \frac{x}{27}$ .

  

The given statements:

  $x\approx 27\times 0.8391$ .

1. $x\approx 27\times 1.1918$ .
2. $x\approx \frac{27}{0.8391}$ .
3. $x\approx \frac{27}{1.1918}$ .

The correct statement is $(\text{b}),x\approx 27\times 1.1918,$ and $(\text{c}),x=\frac{27}{0.8391}$ .

If the given two ways are continued, they will give $(\text{b})$ and $(\text{c})$ as a result.

The easier way would be by choosing $(\text{b}),$ because in $(\text{b})$ the part after the decimal point can be neglected.

Thus, it becomes $27\times 1=27$ .

Conclusion:

Hence, the correct statement is $(\text{b}),x\approx 27\times 1.1918,$ and $(\text{c}),x=\frac{27}{0.8391}$ .