Start with plotting the points in the coordinate plane, and then use the inverse tangent to find the measure of the appropriate angle.
m∠ Y≈ 56.3^(∘)
Practice makes perfect
Let's begin with plotting the given points in the coordinate plane and connecting them to form △ XYZ. Notice that ∠ Z is a right angle.
We are asked to find the measure of ∠ Y. To do this, we can use the fact that the tangent of an angle is the ratio of the length of leg opposite to this angle to the length of leg adjacent to this angle.
tan Y=ZX/ZYTo evaluate the lengths of both segments, we will use the Distance Formula. Let's start with ZX.
The length of ZY is 4sqrt(2). As we found the lengths of both sides, let's substitute these values into our equation.
tan Y=6sqrt(2)/4sqrt(2)
Next, we will rewrite this equation using the inverse tangent.
tan Y=6sqrt(2)/4sqrt(2) ⇓
m∠ Y=tan ^(-1)6sqrt(2)/4sqrt(2)
Now we will solve the above equation.
