CPM Homework Help : CCG Problem 5-18

While shopping at his local home improvement store, Chen noticed that the directions for an extension ladder state, “This ladder is most stable when used at a $\mathit{75º}$ angle with the ground.” He wants to buy a ladder to paint a two-story house that is $26$ feet high. How long does his ladder need to be? Draw a diagram and set up an equation for this situation. Show all work.

Hint:

Draw a diagram comparable to the one below.

Right triangle with vertical leg against side of a house, hypotenuse is labeled, ladder = x, vertical leg labeled 26 feet, angle opposite vertical leg labeled 75 degrees.

More Help:

Refer to the Math Notes box in Lesson 5.1.2 if you need help deciding which trigonometric ratio to use when solving for $x$ .

$\text{length of ladder}=x$