Answer :
The distance from the original boat position to the bottom of the lighthouse is a. The boat travels x distance and ends up b distance from the bottom of the lighthouse.
tan 76.88333 = a/200
a = 200 tan 76.88333 = 858.3177
tan 39.3 = b/200
b = 200 tan 39.3 = 163.6981
x = a - b = 858.3177 - 163.6981 = 694.6196
Answer: 694.62 ft
tan 76.88333 = a/200
a = 200 tan 76.88333 = 858.3177
tan 39.3 = b/200
b = 200 tan 39.3 = 163.6981
x = a - b = 858.3177 - 163.6981 = 694.6196
Answer: 694.62 ft
Answer:
Step-by-step explanation:
We know that from the boat to the top of the lighthouse, it makes a right triangle. The angle between the horizontal line and the diagonal line will make the angle of depression that is 13.116666..
Now, tangent of that angle (tan is opposite over adjacent) is=[tex]\frac{200'}{d_{1}}[/tex], therefore
tan(13.1166)=[tex]\frac{200'}{d_{1}}[/tex] (1)
When the boat is at the second position, similarly doing the same way we get: tan(50.7)=[tex]\frac{200'}{d_{2}}[/tex]
Now, the travel distance is given by: [tex]d_{1}- d_{2}[/tex]
[tex]d_{1}=\frac{200}{tan(13.1166)}[/tex] and [tex]d_{2}=\frac{200}{tan(50.7)}[/tex]
Thus, travel distance=[tex]\frac{200}{tan(13.1166)}-\frac{200}{tan(50.7)}[/tex]
=858.32 - 163.70 = 694.62'