A salvage ship’s sonar locates wreckage at a 12 degree angle of depression. A diver is lowered 40 meters to the ocean floor. To the nearest meter how far does the diver need to walk along the ocean floor to the wreckage?

tan 12 = 40/d

d = 40/tan 12 = 188 meters !

If that diver is wearing a hard hat, he is going to be a wreck himself by the time he gets there and it will take so long that he will need to make decompression stops upon ascent to avoid getting the bends.
Move the stupid ship !

thank you first answer I got was 32.03

You are welcome.

please draw that situation

Well, let's dive right into the math, shall we? We have a 12-degree angle of depression and a diver lowered 40 meters. Now, imagine the diver doing the underwater stroll, feeling all fancy.

Using a bit of trigonometry, we can determine the distance the diver needs to walk along the ocean floor. Since we know the angle and the vertical distance, we can use the tangent function. Tangent of 12 degrees is approximately 0.21 (rounded to two decimal places).

So, the diver needs to walk a distance of approximately 40 meters divided by 0.21. Crunching the numbers, we get approximately 190 meters (rounded to the nearest meter).

That's quite an aquatic adventure, isn't it? Just remember to bring some underwater sunscreen and a towel to dry off after the dive!

To find the distance the diver needs to walk along the ocean floor to the wreckage, we can use the trigonometric function tangent.

Let's assume that the distance the diver needs to walk is represented by "x" meters.

From the given information, we know that the angle of depression is 12 degrees, and the diver is lowered 40 meters.

Using the tangent function, we can set up the following equation:

tan(12 degrees) = 40 meters / x meters

Now, to solve for x, we can rearrange the equation:

x meters = 40 meters / tan(12 degrees)

Calculating this, we find:

x meters ≈ 194.97 meters

Thus, to the nearest meter, the diver needs to walk approximately 195 meters along the ocean floor to the wreckage.