Question

The base of a 40-foot ladder is 8 feet from the wall. How high is the ladder on the wall

Answer 1

Answer:

The height of ladder on the wall is 39 feet .

Step-by-step explanation:

Given as :

The measure of the ladder = d = 40 feet

The ladder distance from the wall = x = 8 feet

Let The height of ladder on the wall = h feet

Let The angle made by ladder base with ground = Ф

Now, According to question

cos angle = $\dfrac{\textrm base}{\textrm hypotenuse}$

Or, cos Ф = $\dfrac{\textrm x}{\textrm d}$

Or, cos Ф = $\dfrac{\textrm 8 feet}{\textrm 40 feet}$

Or, cos Ф = $\dfrac{\textrm 1 }{\textrm 5 }$

∴ Ф = $cos^{-1}0.2$

Now, Again

Sin angle = $\dfrac{\textrm perpendicular}{\textrm hypotenuse}$

Or, sin Ф = $\dfrac{\textrm h}{\textrm d}$

Or, sin Ф = $\dfrac{\textrm h feet}{\textrm 40 feet}$

Or, sin  $cos^{-1}0.2$ = $\dfrac{\textrm h }{\textrm 40 }$

Or, 0.9797 =  $\dfrac{\textrm h }{\textrm 40 }$

∴  h = 0.9797 × 40

i.e h = 39.188 feet

So, The height of ladder on wall = h = 39 feet

Hence, The height of ladder on the wall is 39 feet . Answer