Answer :
Answer:
The depth of the shipwreck is 100.29 feet.
Explanation:
We can determine the depth of the shipwreck by looking at the attached picture:
- Point A is where the diver is 20 feet below the surface.
- Point B is where the diver is 45 feet above the ocean floor.
- Point C is where the shipwreck is located.
For ΔACD:
[tex]\displaystyle tan(70^o)=\frac{AC}{CD}[/tex]
[tex]\displaystyle tan(70^o)=\frac{45+y}{x}[/tex]
[tex]\displaystyle x=\frac{45+y}{tan(70^o)}[/tex] ... [1]
For ΔBCD:
[tex]\displaystyle tan(57^o)=\frac{BC}{CD}[/tex]
[tex]\displaystyle tan(57^o)=\frac{45}{x}[/tex]
[tex]\displaystyle x=\frac{45}{tan(57^o)}[/tex] ... [2]
Since [tex]x[/tex] in [1] equals to [tex]x[/tex] in [2], then:
[tex]\displaystyle \frac{45+y}{tan(70^o)}=\frac{45}{tan(57^o)}[/tex]
[tex]\displaystyle 45+y=\frac{tan(70^o)(45)}{tan(57^o)}[/tex]
[tex]\displaystyle y=\frac{tan(70^o)(45)}{tan(57^o)}-45[/tex]
[tex]y=35.29\ ft[/tex]
The depth of the shipwreck:
[tex]depth=20+y+45[/tex]
[tex]=20+35.29+45[/tex]
[tex]=\bf 100.29\ ft[/tex]
