# The sail on a toy boat is in the shape of an isosceles triangle. Its legs are 12 inches long and its base angles measure 70°. How long to the nearest hundredth of an inch, is the base of the sail?

##### 1 Answer

base

#### Explanation:

If we were to cut the whole isosceles triangle in half, two right triangles would be produced:

Using a **primary trigonometric ratio** , we can determine the base length of one of the right triangles. In this case, we can use **cosine**. Recall that:

#costheta="adjacent"/"hypotenuse"#

To find the base length, or the "adjacent," substitute your known values into the formula:

#costheta="adjacent"/"hypotenuse"#

#cos70^@="adjacent"/12#

#12(cos70^@)="adjacent"#

#"adjacent"~~4.10# #"inches"# #rArr# rounded off to two decimal places

Recall that the base length of the left triangle is equal to the base length of the right triangle. Thus, multiply

#4.10*2#

#~~8.20# #"inches"#