From the top of the offshore that is 153 feet above sea level the angle of depression of a passing ship is 36 degrees. what is the distance between the ship and the top of the oil rig?

Question

Samantha Abate · Accepted Answer

#260.299\ ext{feet# Consider the right triangle with acute angle # heta=36^\circ# & the opposite leg #153#. Then get the length of hypotenuse #=153/\sin36^\circ# #=153/{\sqrt{10-2\sqrt5}/4}# #=612/\sqrt{10-2\sqrt5}# #=260.299# The distance between the top of oil rig & the ship will be equal to the length of hypotenuse #260.299\ ext{feet#

Madelyn Adams · Answer

undefined To find the distance between the ship and the top of the oil rig, we can use trigonometry, specifically the tangent function.

Given that the angle of depression is 36 degrees, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.

Let $ d $ be the distance between the ship and the top of the oil rig. Then, we have:

$$ \tan(36^\circ) = \frac{153}{d} $$

We can rearrange this equation to solve for $ d $:

$$ d = \frac{153}{\tan(36^\circ)} $$

Now, we can calculate the value of $ d $:

$$ d = \frac{153}{\tan(36^\circ)} \approx \frac{153}{0.7265} \approx 210.40 $$

Therefore, the distance between the ship and the top of the oil rig is approximately 210.40 feet.