Chapter 8.5, Problem 9CE

a.

To determine

To express $\tan {60}^0$ in the simplest radicle form.

Answer to Problem 9CE

  $\sqrt{3}$

Explanation of Solution

Given:

Three ${30}^0,{60}^0,{90}^0$ triangles

  

Formula used:

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

In triangle 1:

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

  $\Rightarrow \tan {60}^0=\frac{3\sqrt{3}}{3}$

  $\Rightarrow \tan {60}^0=\sqrt{3}$

In triangle 2:

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

  $\Rightarrow \tan {60}^0=\frac{5\sqrt{3}}{5}$

  $\Rightarrow \tan {60}^0=\sqrt{3}$

In triangle 3:

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

  $\Rightarrow \tan {60}^0=\frac{t\sqrt{3}}{t}$

  $\Rightarrow \tan {60}^0=\sqrt{3}$

Conclusion:

Therefore, the simplest radical form of $\tan {60}^0$ is $\sqrt{3}$ .

b.

To determine

To find the appropriate value for $\tan {60}^0$ .

Answer to Problem 9CE

The approximate value of $\tan {60}^0$ is 1.732051.

Explanation of Solution

Given:

Three ${30}^0,{60}^0,{90}^0$ triangles

Calculation:

  $\sqrt{3}\approx 1.732051$ (given)

  $\Rightarrow \tan {60}^0=\sqrt{3}$

  $\Rightarrow \tan {60}^0=1.732051$ (approximately)

Conclusion:

Therefore, the approximate value of $\tan {60}^0$ is 1.732051.

c.

To determine

To check whether the value of $\tan {60}^0$ mentioned in page 311 is matching with above answer or not.

Answer to Problem 9CE

Correct

Explanation of Solution

Given: Three ${30}^0,{60}^0,{90}^0$ triangles

  

From above sub parts, $\tan {60}^0=\mathrm{1.732051.}$

Value of $\tan {60}^0$ in page 311 = $1.732$ .

Calculation:

From above sub parts, the value of $\tan {60}^0$ is 1.732051.

Rounding it to 4 decimal places,

  $\tan {60}^0=1.732$

The value of $\tan {60}^0$ in page 311 = $1.732$ .

Here, both values are equal to each other.

Conclusion:

Therefore, the given value is correct.