You are standing on a cliff that is 50 m above the ocean and you see a ship that is 950 m from the bottom of the cliff. Find the angle of depression from you to the ship. Round your answer to the nearest tenth of a degree.
To find the angle of depression, we need to use trigonometry. The angle of depression is the angle formed between the horizontal line and the line of sight (or line of sight extended) from the observer (you) down to the object (the ship). In this case, the object is the ship.
To find this angle, we can use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right triangle.
In this scenario, the observer (you) are standing on a cliff that is 50 m high, and you see a ship that is 950 m from the bottom of the cliff. To create a right triangle, we can connect the top of the cliff (observer's position) to the bottom of the cliff (ship).
The height of the cliff (opposite side) is 50 m, and the distance from the bottom of the cliff to the ship (adjacent side) is 950 m. Therefore, we have:
Tan(angle) = opposite/adjacent
Tan(angle) = 50/950
To solve for the angle, we can use the inverse tangent (arctan) function. Taking the inverse tangent of both sides of the equation gives us:
Angle = arctan(50/950)
Using a scientific calculator, we can find the arctan of 50/950.
Angle ≈ 2.967 degrees
Rounding this to the nearest tenth of a degree, the angle of depression from you to the ship is approximately 3.0 degrees.
The cliff makes a right angle with the ocean. The two legs are 50m (the cliff) and 950m (distance on the ocean from the cliff to the ship).
Draw the triangle for that, the rest follows.