Round your answer to three significant digits.
Use the distances shown in the following figure to determine the depth of the submarine below the surface of the water. Assume that the line segment between the surface ships is directly above the submarine.
a = 719
b = 585
c = 445
356
To determine the depth of the submarine below the surface of the water, we can use the concept of trigonometry and the Pythagorean theorem.
Step 1: Identify the triangle formed by the surface ships and the submarine. In this case, it is a right triangle since the line segment between the surface ships is directly above the submarine.
Step 2: Label the sides of the triangle. Let c represent the depth of the submarine, a represent the distance between the first surface ship and the submarine, and b represent the distance between the second surface ship and the submarine.
Step 3: Apply the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, c is the hypotenuse, so we have the equation c^2 = a^2 + b^2.
Step 4: Substitute the given values into the equation. We are given a = 719 and b = 585. Plugging these into the equation, we get c^2 = (719)^2 + (585)^2.
Step 5: Calculate c^2 using a calculator or math software. In this case, c^2 = 518,161 + 342,225 = 860,386.
Step 6: Take the square root of both sides of the equation to isolate c. Using a calculator or math software, the square root of 860,386 is approximately 928.746.
Step 7: Round your answer to three significant digits. In this case, the answer would be 929.
Therefore, the depth of the submarine below the surface of the water is approximately 929 units.