# A ladder leans against a vertical wall & its 9 meters up the wall. If the ladder is at an angle of elevation 60 degrees to the horizontal, how do you calculate the distance the foot of the ladder is from the base of the wall?

Feb 26, 2018

$\text{distance "=5.20" feet to 2 dec. places}$

#### Explanation:

$\text{we consider the angle between wall/horizontal to be}$
$\text{a right angle}$

$\text{using "color(blue)"trigonometric ratio}$

$\tan {60}^{\circ} = \text{opposite"/"adjacent}$

$\text{where opposite "=9" and adjacent } = x$

$\text{x is the distance of foot of ladder from wall}$

$\Rightarrow \tan {60}^{\circ} = \frac{9}{x}$

$\Rightarrow x = \frac{9}{\tan {60}^{\circ}} \approx 5.20 \text{ feet to 2 dec. places}$

Feb 26, 2018

See below.

#### Explanation:

The tangent function in relation to the sides of a right triangle is:

$\tan \left(\theta\right) = \text{opposite"/"adjacent}$

From the diagram we are looking for $\boldsymbol{x}$

$\tan \left(60\right) = \text{opposite"/"adjacent} = \frac{9}{x}$

Rearranging:

$x = \frac{9}{\tan} \left(60\right) = 5.2$ metres 2 .d.p.