A tourist looks from the observation deck of the space needle in Seattle. The deck is at a height of 520ft. She sees her friend on the ground below at an angle of depression of 83.1 degrees. What is the distance between the two? Round to the nearest tenth of a foot.

Options:
526.6
523.8
516.2
62.9

I think the answer is b but I’m not sure some help please :/

b is correct

sike no it ain't

No, b is not correct.

Well, let me tell you, I've always got my head in the clouds, so this question is right up my alley! To find the distance between the tourist on the observation deck and her friend on the ground, we can use a little bit of trigonometry.

First, we need to find the length of the opposite side, which is the height of the observation deck, 520 ft.

Then, we need to find the length of the adjacent side. This side represents the horizontal distance between the tourist and her friend. We can use the tangent function to find it.

The tangent of the angle of depression (83.1 degrees) is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 520 ft, and we want to find the length of the adjacent side.

Using some magical math powers, we can rearrange the equation to solve for the adjacent side:

Adjacent side = opposite side / tangent(angle of depression)

Adjacent side = 520 ft / tangent(83.1 degrees)

Calculating that gives us approximately 62.919 ft, which is rounded to 62.9 ft.

So, the correct answer is option D, 62.9.

Now, don't fret if math isn't your strong suit, I'm always here to clown around and lend a helping hand!

To find the distance between the tourist and her friend on the ground, we can use trigonometry.

First, we need to understand the concept of the angle of depression. The angle of depression is the angle formed between the line of sight from an observer to a point below the observer's horizontal line of sight. In this case, the angle of depression is 83.1 degrees.

Now, let's define some variables:
- Let "d" represent the distance between the tourist and her friend on the ground.
- Let "h" represent the height of the observation deck, which is given as 520ft.

Using trigonometry, we can set up a tangent equation. The tangent of the angle of depression is equal to the opposite side (height of the observation deck) divided by the adjacent side (distance between the two):

tan(83.1 degrees) = h / d

Now, we can solve for "d". Rearrange the equation to solve for d:

d = h / tan(83.1 degrees)

Substituting the given values, we have:

d = 520 ft / tan(83.1 degrees)

Using a scientific calculator, evaluate the tangent of 83.1 degrees. You should get approximately 5.2338.

d = 520 ft / 5.2338 ≈ 99.3 ft

The distance between the tourist and her friend on the ground is approximately 99.3 feet. But since we need to round to the nearest tenth of a foot, the correct answer is 99.3 feet, rounded to 99.0 feet.

Therefore, the correct option is c) 516.2.

correct