$\"\"$

(a)

Find an equation in terms of tangent $\"\"$ .

From the given figure :

Opposite side $\"\"$ and adjacent side $\"\"$ .

$\"\"$ .

$\"\"$

Multiply each side by $\"\"$ .

$\"\"$ .

The equation in terms of tangent $\"\"$ is $\"\"$ . $\"\"$

(b)

The equation is $\"\"$ .

Consider right hand side of the equation : $\"\"$ .

Co-function identity : $\"\"$ .

$\"\"$

Quotient identity : $\"\"$ .

$\"\"$

From (a), $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

= Left hand side of the equation.

$\"\"$

(c)

Consider $\"\"$ .

Solve for $\"\"$ .

$\"\"$

Here, $\"\"$ feet.

Complete the below table for given values of $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$

$\"\"$

(d)

If $\"\"$ , then $\"\"$ .

From the above calculation conclude that, if $\"\"$ , then $\"\"$ will be greater than $\"\"$ .

If $\"\"$ , then $\"\"$ .

From the above calculation conclude that, if $\"\"$ , then $\"\"$ will be less than $\"\"$ .

Since $\"\"$ is between $\"\"$ and $\"\"$ , if $\"\"$ , then $\"\"$ will be $\"\"$ .

The sites with widths of 5 feet and 140 feet could not be used, because $\"\"$ and $\"\"$ respectively.

The site with a width of 35 feet could be used because $\"\"$ .

$\"\"$

(a).

The equation in terms of tangent $\"\"$ is $\"\"$ .

(b).

The equation $\"\"$ represents an identity.

(c).

The completed table is :

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$
$\"\"$	$\"\"$

(d).

The sites with widths of 5 feet and 140 feet could not be used.

The site with a width of 35 feet could be use.