Let's begin with recalling the definition of the tangent of an angle.
If△ ABCis a right triangle with acute∠A,
then the tangent of∠Ais the ratio of the length of the leg opposite∠A to the length of the leg adjacent∠A.
Now let's look at the given picture. We are given that Sofia wants to put a flower bed in the corner of her yard by laying a stone border that starts 3 feet from the corner of one fence and ends 6 feet from the corner of the other fence.
We are asked to evaluate the measures of angles x and y. To do this, we can write equations for tan x and tan y using the definition we recalled.
tan x=6/3
tan y=3/6
Next we can rewrite these equations using the inverse tangent, and then we will find the values of x and y using a calculator.
x=tan^(-1)6/3≈ 63.4^(∘)
y=tan^(-1) 3/6≈ 26.6^(∘)
