# Help me with this question?

## My teacher requires work if it is not too much of a hassle please SHOW WORK!!!! thank you for helping.

Mar 25, 2017

$x = 5.8 c m$ if that is the question.

The other answers are $A =$23.2cm^2$\mathmr{and}$V = 162.4 cm^3#, but the given formula is incorrect for either area or volume.

#### Explanation:

If you have to find $x$ using trig ratios, you need to know that you are working with the acute angle $\angle$ at the $b a s e$ of a right angle triangle.

The value of this angle is $36$ degrees.

The trig ratio (mentioned in the question) that you want to apply is called the 'tangent' and it has the following properties:

when comparing sides of a right angle triangle to an acute angle

2) Value: Tangent 36 degrees = $.727$

When we substitute the given values into equation 1):

$.727 = \frac{x}{8 c m}$

$.727 \left(8 c m\right) = x$

$5.8 c m = x$

The Area $A$ of the Right Triangle shown using the correct formula is:

$A = \frac{1}{2} \cdot b h = \frac{1}{2} \cdot 8 c m \cdot 5.8 c m = 4 \cdot 5.8 = 23.2 c {m}^{2}$

If you need to find the Volume $V$ of the Right Triangular Prism shown, you will need one more step using the correct formula;

$V = \left(\frac{1}{2} b h\right) w$ where we have introduced $w$ for width.

When we substitute the given values into this equation:

$v = \frac{1}{2} \cdot 8 c m \cdot 5.8 \left(c m\right) \cdot 7 c m = 7 \left(23.2\right) c {m}^{3} = 162.4 c {m}^{3}$