Question

While shopping at his local home improvement store, Chen notices that the directions for an extension ladder state, “This ladder is most stable when usedat a 75° angle with the ground." He wants to buy a ladder that will reach a height of 26 feet to paint a two-story house. How long does his ladder need tobe? Draw a diagram and set up an equation for this situation. Show all work.

Answer 1

hello

to solve this question, we need to draw a diagram to illustrate their positions

to solve this question, we can simply use trigonometric ratio

SOHCAHTOA

$\begin{gathered} \sin \theta=\frac{opp}{hyp} \\ \cos \theta=\frac{adj}{hyp} \\ \tan \theta=\frac{opp}{adj} \end{gathered}$

from this, we can use the sine angle to solve this since the parameters of interests are hypothenus, opposite and angle

$\begin{gathered} \theta=75 \\ \text{hpy}=x \\ \text{opp}=26 \end{gathered}$$\begin{gathered} \sin 75=\frac{26}{x} \\ x=\frac{26}{\sin 75} \\ x=26.917\text{feet} \end{gathered}$

from the calculations above, the length of the ladder is 26.91 feet