Chapter 8.5, Problem 8CE

a.

To determine

To express $\tan 60°$ in the simplest radicle form.

Answer to Problem 8CE

  $\sqrt{3}$ .

Explanation of Solution

Given:

Three $30°,60°,90°$ triangles,

  

Formula used:

  $\tan \theta =\frac{perpendicular}{base}$

In triangle 1:

  $\tan \theta =\frac{perpendicular}{base}$ ,

  $\Rightarrow \tan 60°=\frac{3\sqrt{3}}{3},$

  $\Rightarrow \tan 60°=\sqrt{3}$ .

In triangle 2:

  $\tan \theta =\frac{perpendicular}{base}$ ,

  $\Rightarrow \tan 60°=\frac{5\sqrt{3}}{5}$ ,

  $\Rightarrow \tan 60°=\sqrt{3}$ .

In triangle 3:

  $\tan \theta =\frac{perpendicular}{base}$

  $\Rightarrow \tan 60°=\frac{t\sqrt{3}}{t}$ ,

  $\Rightarrow \tan 60°=\sqrt{3}$ .

Conclusion:

Therefore, the simplest radical form of $\tan 60°$ is $\sqrt{3}$ .

b.

To determine

To find the appropriate value for $\tan 60°$ .

Answer to Problem 8CE

The approximate value of $\tan 60°$ is 1.732051.

Explanation of Solution

Given information:

Three $30°,60°,90°$ triangles,

Calculation:

Since $\sqrt{3}\approx 1.732051$ ,

  $\Rightarrow \tan 60°=\sqrt{3}$ ,

  $\Rightarrow \tan 60°=1.732051$ (approximately).

Conclusion:

Therefore, the approximate value of $\tan 60°$ is 1.732051.

c.

To determine

To check whether the value of $\tan 60°$ mentioned in page 311 is matching with above answer.

Answer to Problem 8CE

Correct.

Explanation of Solution

Given:

Three $30°,60°,90°$ triangles,

From above sub − parts, $\tan 60°=\mathrm{1.732051.}$

Also, the value of $\tan 60°$ in page 311 = $1.732$ .

Calculation:

Since, $\tan 60°=1.732051$ , then −

Rounding it to four decimal places, we have −

  $\tan 60°=1.732$ , and

The value of $\tan 60°$ in page 311 = $1.732$ .

Hence, both values are equal to each other.

Conclusion:

Therefore, the given value is correct.