Questions: An aerial photographer who photographs real estate properties has determined that the best photo is taken at a height of approximately 437 ft and a distance of 820 ft from the building. What is the angle of depression from the plane to the building? The angle of depression from the plane to the building is 0° (Round to the nearest degree as needed.)

An aerial photographer who photographs real estate properties has determined that the best photo is taken at a height of approximately 437 ft and a distance of 820 ft from the building. What is the angle of depression from the plane to the building?

The angle of depression from the plane to the building is 0° (Round to the nearest degree as needed.)

Transcript text: An aerial photographer who photographs real estate properties has determined that the best photo is taken at a height of approximately 437 ft and a distance of 820 ft from the building. What is the angle of depression from the plane to the building? The angle of depression from the plane to the building is $\square$ $0^{\circ}$ (Round to the nearest degree as needed.)

Solution

Solution Steps

Step 1: Identify the right triangle components

The problem involves a right triangle where:

The height (opposite side) is 437 ft.
The distance from the building (adjacent side) is 820 ft.
The angle of depression (θ) is what we need to find.

Step 2: Use the tangent function

The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Therefore, we use the tangent function: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{437}{820} \]

Step 3: Calculate the angle

To find the angle θ, take the arctangent (inverse tangent) of the ratio: \[ \theta = \tan^{-1}\left(\frac{437}{820}\right) \]

Step 4: Compute the value

Using a calculator: \[ \theta \approx \tan^{-1}(0.5329) \approx 28.1^\circ \]