. A spotlight is mounted on a wall 7.4 feet above the floor in an office building. It is used to light a door 9.3 feet from the wall. To the nearest degree, what is the angle of depression from the spotlight to the bottom of the door? (1 point). A) 39 degrees. B) 51 degrees. C) 53 degrees. D) 37 degrees

Question

. A spotlight is mounted on a wall 7.4 feet above the floor in an office building. It is used to light a door 9.3 feet from the wall. To the nearest degree, what is the angle of depression from the spotlight to the bottom of the door? (1 point). A) 39 degrees. B) 51 degrees. C) 53 degrees. D) 37 degrees

Answer 1

We can use trigonometry to solve this problem. Let's draw a diagram:

```
spotlight
*
|\
| \
| \ door
| \
| \
| \
| \
| \
| \
| \
|theta \
------------
distance
```

We want to find the angle theta. We know the opposite side (the height of the spotlight above the floor) and the adjacent side (the distance from the spotlight to the door). We can use the tangent function:

```
tan(theta) = opposite/adjacent
tan(theta) = 7.4/9.3
theta = arctan(7.4/9.3)
theta ≈ 39 degrees
```

Therefore, the answer is A) 39 degrees (rounded to the nearest degree).

Answer 2

To find the angle of depression, we can use the tangent function:

tan(angle) = opposite/adjacent

In this case, the opposite side is the height of the spotlight above the floor (7.4 feet) and the adjacent side is the distance from the wall to the door (9.3 feet).

tan(angle) = 7.4/9.3

Now we can find the angle by taking the inverse tangent (arctan) of both sides:

angle = arctan(7.4/9.3)

Using a calculator, the angle is approximately 39 degrees.

Therefore, the correct answer is A) 39 degrees.

Answer 3

To find the angle of depression from the spotlight to the bottom of the door, we can use trigonometry. The angle of depression is the angle formed between the line of sight from the spotlight to the bottom of the door and a horizontal line.

First, let's define a right-angled triangle. The side opposite the angle of depression is the vertical distance from the spotlight to the floor, which is 7.4 feet. The side adjacent to the angle of depression is the horizontal distance from the spotlight to the door, which is 9.3 feet.

We can use the tangent function to calculate the angle of depression. The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

So, the tangent of the angle of depression can be found using the formula:

tan(angle) = opposite / adjacent

tan(angle) = 7.4 / 9.3

Now, we can solve for the angle by taking the inverse tangent (also known as arctan) of both sides:

angle = arctan(7.4 / 9.3)

Using a calculator, we find:

angle ≈ 39.3 degrees

Since we need to round to the nearest degree, the angle of depression from the spotlight to the bottom of the door is approximately 39 degrees.

Therefore, the correct answer is:

A) 39 degrees.

Answer 4

Well, let's shed some light on this question! First, let's imagine that the spotlight is casting a straight beam of light onto the bottom of the door. We can then form a right triangle with the spotlight, the bottom of the door, and the floor.

The opposite side of the triangle is the distance from the spotlight to the bottom of the door, which is 9.3 feet. The adjacent side is the vertical distance from the spotlight to the floor, which is 7.4 feet.

Now, we can use the angle of depression to find the angle between the hypotenuse and the adjacent side of the triangle. We know that tan(angle) = opposite/adjacent.

Using this information, we can calculate: tan(angle) = 9.3/7.4.

Taking the inverse tangent (arctan) of both sides gives us the angle: angle = arctan(9.3/7.4) ≈ 51 degrees.

So, to the nearest degree, the angle of depression from the spotlight to the bottom of the door is approximately 51 degrees.

Therefore, the answer is B) 51 degrees.