Solve the problem.
-An 8-foot-tall digital display showing airport arrivals and departures is mounted on a wall so that the bottom of the display is 12 feet above the floor. A woman whose eyes are 5 feet above the floor stands 42 feet away from
The wall. Find the angle (to the nearest degree) between the top and bottom of the display as seen by the
Woman.

Question

Solve the problem.
-An 8-foot-tall digital display showing airport arrivals and departures is mounted on a wall so that the bottom of the display is 12 feet above the floor. A woman whose eyes are 5 feet above the floor stands 42 feet away from
The wall. Find the angle  (to the nearest degree) between the top and bottom of the display as seen by the
Woman.

Quizplus · Accepted Answer

We can use trigonometry to solve for the angle between the top and bottom of the display as seen by the woman. Let's call this angle θ.

First, let's draw a right triangle with the woman at one vertex, the bottom of the display at another vertex, and the top of the display at the third vertex. We can label the distance from the woman to the wall as x.

Using the Pythagorean theorem, we can find the height of the display above the woman's eyes:
√(8^2 + x^2)

We can also find the height of the woman's eyes above the floor:
5

Now we can use trigonometry to solve for θ:
tan(θ) = opposite/adjacent
tan(θ) = (8 + √(8^2 + x^2) - 5) / x
tan(θ) = (8 + √(64 + x^2) - 5) / x
tan(θ) = (3 + √(64 + x^2)) / x

Plugging in x = 42, we get:
tan(θ) = (3 + √(64 + 42^2)) / 42
tan(θ) ≈ 0.217

Taking the inverse tangent, we get:
θ ≈ 12.5 degrees

Since the question asks for the angle to the nearest degree, the best choice is B, 12 degrees. Using trigonometry, we can find that the distance from the floor to the top of the display is 20 feet. Then, we can set up a right triangle with the height of the display (8 feet), the distance from the woman to the wall (42 feet), and the distance from the floor to the woman's eyes (5 feet). Solving for the angle opposite the height of the display, we get approximately 24 degrees. However, this is just half of the angle between the top and bottom of the display, so we multiply by 2 to get 48 degrees. Rounded to the nearest degree, the answer is B.

Solve the Problem. -An 8-Foot-Tall Digital Display Showing Airport Arrivals and Departures Is