# A ladder 36m long rests against a wall, its foot being at a horizontal distance of 25m from the base of the wall. What angle does the ladder make with the ground?

##### 2 Answers
Mar 7, 2018

The ladder makes ${46.02}^{0}$ angle with the ground.

#### Explanation:

In the right triangle formed by the ladder, wall and ground, base is

$b = 25$ m , hypotenuse is $h = 36$ m. Let the angle formed by the

ladder with the ground is $\theta \therefore \cos \theta = \frac{b}{h} = \frac{25}{36}$

$\therefore \theta = {\cos}^{-} 1 \left(\frac{25}{36}\right) \mathmr{and} \theta \approx {46.02}^{0}$

The ladder makes ${46.02}^{0}$ angle with the ground. [Ans]

Mar 7, 2018

0.803" radians"color(white)("xx")=color(white)("xx")46.0^circ (approx.)

#### Explanation:

By basic trig definitions (for the above diagram):
$\textcolor{w h i t e}{\text{XXX}} \cos \left(\theta\right) = \frac{25}{36}$
and
$\textcolor{w h i t e}{\text{XXX}} \arccos \left(\frac{25}{36}\right) = \theta$

That is
color(white)("XXX")theta=arccos(25/36)=arccos(0.69bar4)=0.803" radians" (using a calculator to 3 decimal places)