a We are asked to sketch a diagram of the described situation. To do this, let's notice that the vertical viewing angle of Natalie's camera is set for 90^(∘). Therefore, we will use a right triangle to sketch a diagram describing the given situation.
The vertex B represents the camera, the vertex A represents the top of the subject, and the vertex C represents the bottom of the subject. The segment BD is the line of vision of the camera.
b In this part, we are asked to determine how far away from the truck Natalie should stand so that she perfectly frames the entire height of the truck in her shot. Looking at the diagram we sketched in the previous part, we can see that the answer for this question is the length of BD.
As we can see, the length of BD is the altitude of a right triangle ABC. Therefore, the Geometric Mean Altitude Theorem can be useful. Let's recall it.
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.
This means that the length of BD is the geometric mean of the lengths of DC and AD.
BD=sqrt(DC* AD)
We are given that a tripod is 5 feet above ground level. This means that the length of DC is also 5 feet. Therefore, the length of AD will be the difference between the length of AC and the length of DC.
AD= 15ft6in.- 5ft=10ft6in.=10.5ft
Let's substitute the measures that we found into the equation and find the length of BD.
