Answer:
The angle of depression formed by Darius's sight line to the ranger station is 53.13°.
Step-by-step explanation:
Denote Darius's camp site as C, the ranger station as R and the tree as T.
Consider the triangle CTR.
TX is the altitude of the right angled triangle TXR.
The altitude of a right angled triangle forms two triangle that similar to each other.
So, ΔTXC [tex]\sim[/tex] ΔTXR.
Compute the measure of TX as follows:
[tex]\frac{CX}{TX}=\frac{TX}{RX}\\\\TX^{2}=CX\times RX\\\\TX=\sqrt{CX\times RX}[/tex]
[tex]=\sqrt{18\times 32}\\\\=24\ \text{yd}[/tex]
The angle d represents the angle of depression formed by Darius's sight line to the ranger station.
Compute the value of d as follows:
[tex]tan\ d^{o}=\frac{RX}{TX}\\\\d^{o}=tan^{-1} [\frac{RX}{TX}][/tex]
[tex]=tan^{-1} [\frac{32}{24}]\\\\=53.13[/tex]
Thus, the angle of depression formed by Darius's sight line to the ranger station is 53.13°.
