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.
X = 1450 Ft.
Y = 850 Ft.
Tan A = Y/X.
663
To find the angle x, we can use trigonometry.
Let's consider a right triangle formed by the ship, the point on the ocean's surface, and the submarine. The side opposite to the angle x is the depth of the submarine (880 ft), and the side adjacent to the angle x is the distance between the ship and the point on the ocean's surface (1450 ft).
Using the tangent function, which is defined as the ratio of the opposite side to the adjacent side, we can write:
tan(x) = opposite/adjacent
tan(x) = 880/1450
Now we can use the inverse tangent function (arctan) to find the angle x. This function will give us the angle whose tangent is equal to the ratio we calculated earlier:
x = arctan(880/1450)
Calculating this using a scientific calculator, we find:
x ≈ 30.1 degrees
Therefore, the angle x to the nearest degree is 30 degrees.