A ship’s sonar detects a submarine 880 feet below a point on the ocean’s surface 1450 ft dead ahead of the ship. To the nearest degree, find the angle x.

I can't see your diagram and don't know where x is, but I will assume that the data results in a right-angled triangle with x as the angle of depression from the ocean's surface to the sub.

tanx = 880/1450 = ...
x = appr 31.25°

To find the angle x, we can use the concept of trigonometry. Let's consider a right triangle with the ship on the surface of the ocean, the point directly above the submarine, and the submarine itself.

We can label the distance from the ship to the point directly above the submarine as A (1450 ft) and the depth of the submarine as B (880 ft). The distance from the ship to the submarine, which is the hypotenuse of the triangle, can be labeled as C.

Since we have two sides of the right triangle, we can use the trigonometric function tangent (tan) to find the angle x. The tangent of an angle is the ratio of the opposite side to the adjacent side.

In this case, tan(x) = B / A, where B is the opposite side and A is the adjacent side.

Plugging in the given values, we get tan(x) = 880 / 1450.

Now, we can find the angle x by taking the inverse tangent (arctan) of both sides of the equation:

x = arctan(880 / 1450).

Using a calculator or a trigonometric table, we can find the value of arctan(880 / 1450) ≈ 30.13 degrees.

Therefore, to the nearest degree, the angle x is approximately 30 degrees.

To find the angle x, we can use the tangent function because we have the lengths of the opposite and adjacent sides of a right triangle.

Let's label the sides of the right triangle formed by the ship, the point on the ocean's surface, and the submarine:
Opposite side (O) = 880 ft (the depth of the submarine)
Adjacent side (A) = 1450 ft (distance from the ship to the point on the ocean's surface)

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Therefore, we have tan(x) = O / A.

Now, let's plug in the values:
tan(x) = 880 / 1450.

To find the angle x, we need to take the inverse tangent (arctan) of both sides of the equation:
x = arctan(880 / 1450).

Using a calculator, we find:
x ≈ 31.8 degrees.

Therefore, to the nearest degree, the angle x is approximately 32 degrees.