A tourist viewing Sydney Harbour from a building 180 metres above sea level observes a ferry which is 850 metres from the base of the building.Find the angle of depression of his line of sight.

We draw and solve a rt. triangle:

Y = 180 m. = Ht.
X = 850 m = Hor..Distance of ferry.
Z = Hyp. = Line of sight.

tanA = Y/X = 180/850 = 0.21176.
A = 12o = Angle of depression.

A tourist viewing Sydney Harbour from a building 130 metres above sea level observes a ferry which is 800 metres from the base of the building.Find the angle of depression of his line of sight.

To find the angle of depression, we need to use trigonometry. The angle of depression is the angle formed between the line of sight and a horizontal line.

In this case, we have a right triangle formed by the line of sight, the distance from the base of the building to the ferry, and the vertical distance from the building to the ferry. The vertical distance is the height of the building above sea level.

Let's label the angle of depression as θ, the distance from the base of the building to the ferry as x, and the height of the building as h.

Using trigonometry, we can say that:

tan(θ) = h / x

We are given that h = 180 meters and x = 850 meters. Plugging these values into the equation, we can solve for θ:

tan(θ) = 180 / 850

To find the value of θ, we can take the inverse tangent (arctan) of both sides:

θ = arctan(180 / 850)

Using a calculator, we find that arctan(180 / 850) is approximately 11.65 degrees.

Therefore, the angle of depression of the tourist's line of sight is approximately 11.65 degrees.

To find the angle of depression, we need to determine the triangle formed by the tourist's line of sight to the ferry.

We have the following information:
- The height of the building is 180 meters above sea level.
- The distance from the base of the building to the ferry is 850 meters.

The angle of depression is the angle between the line of sight and the horizontal line. The tangent of the angle of depression can be calculated using the formula:

tan(angle) = opposite/adjacent

In this case, the height of the building is the opposite side, and the distance from the base of the building to the ferry is the adjacent side.

Let's calculate the angle of depression:

tan(angle) = 180/850

Now, we need to find the value of the angle by taking the inverse tangent (arctan) of both sides of the equation:

angle = arctan(180/850)

Using a scientific calculator, we find the approximate angle to be 11.09 degrees.

Therefore, the angle of depression from the tourist's line of sight is approximately 11.09 degrees.