Let's begin with recalling the Geometric Mean Altitude Theorem.
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of this altitude is the geometric mean between the lengths of these two segments.
Now, let's take a look at the given picture. We will label the vertices with consecutive letters. Let x represents the height of the waterfall above Makayla's eye level.
As we can see, BD is an altitude of a right triangle ABC. Therefore, we can write that the length of BD is the geometric mean between the lengths of AD and DC.
DB=sqrt(AD * DC)
28=sqrt(x* 5)
Next, we will solve the above equation for x using inverse operations.
The length of AD is 156.8 feet. With this information, we can evaluate the height of the watefall. To do this, we will add the lengths of AD and DC.
156.8ft+ 5ft=161.8ft
The height of the waterfall is 161.8 feet.
