A salvage ship's sonar locates wreckage at a 12 angle of depression. A driver is lowered 40m to the ocean floor. How far does the driver need to walk along the ocean floor to the wreckage?
geez - impatient much?
You have a right angle triangle. Just remember where the angle of depression goes and what it means. Then you have the TAN theta ratio with 40 being the adjacent side, and x being the opposite side. And do the math.
To find the distance the driver needs to walk along the ocean floor to reach the wreckage, we can use trigonometry, specifically the tangent function.
Let's break down the problem step by step:
1. We are given that the angle of depression is 12 degrees. This means that the line of sight, from the salvage ship to the wreckage, is 12 degrees below the horizontal.
2. The driver is lowered 40m to the ocean floor. This forms a right-angled triangle, with the driver on the ocean floor, the salvage ship, and the wreckage forming the three vertices of the triangle.
3. The side opposite to the angle of depression is the depth at which the driver is lowered, which is 40m. Let's denote this side as "opposite."
4. Since we are interested in finding the distance the driver needs to walk along the ocean floor, let's call this distance "adjacent."
5. We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle. In this case, the tangent of angle 12 degrees is equal to the opposite side (40m) divided by the adjacent side (the distance to be determined).
Tan(12°) = opposite / adjacent
6. We need to rearrange the equation to solve for the adjacent side (the distance the driver needs to walk). We can do this by multiplying both sides of the equation by the adjacent side:
Adjacent = opposite / tan(12°)
Substituting the values we have:
Adjacent = 40m / tan(12°)
7. Using a calculator, calculate the value of tangent (12 degrees):
Tan(12°) ≈ 0.2126
8. Now, substitute this value back into the equation:
Adjacent = 40m / 0.2126
9. Perform the division:
Adjacent ≈ 188.36m
Therefore, the driver needs to walk approximately 188.36 meters along the ocean floor to reach the wreckage.