What distance does the boat need to travel on the surface of the ocean to be located directly above the fish?

Question

Help Me Solve this Question! It makes no sense!

A fishing boat determines a pod of fish located in the ocean at an angle of depression of 25° from the current boat location. The fishing boat determines the distance through the ocean to the fish is 150 yards. What distance does the boat need to travel on the surface of the ocean to be located directly above the fish? Sketch the scenario labeling what you know and need to find. Show all work to find the distance. Round to the nearest unit.

I need someone to help me solve this before it's midnight!

Answer 1

Hi Shane,

Like Allen said, imagine a right triangle with the long leg of the triangle representing the surface of the water. It should look something like this:

x

boat _________________

* 25° ⌊|

* |

* |

150 yd * | pod of fish

The hypotenuse, which runs between the boat's current location on the surface of the water and the pod of fish below the water's surface, is 150 yards in distance and intersects the long leg of the triangle at an angle of 25°.

Finally, the short leg of the right triangle runs between the boat's planned location on the surface directly above the pod of fish and the pod of fish.

We are asked to find the distance on the surface of the water between the boat's current or initial location 150 yards away from the pod and it's planned or final location directly above the pod of fish; we'll call this distance x.

Notice from the diagram that cos(25°) = x / 150 because cos(θ) = adjacent/hypotenuse.

Therefore, x = 150 * cos(25°).

Using a calculator, we find that x = 136 yards.