A man is standing in the corridor of a ten storey building and looking at a tall tree in front of the building he sees the top of the tree at an angle of depression 30degree if the tree is 200metre tall and the man's eyes are 300metre above the ground calculate the angle of depression of the foot of the tree as seen by the man

Question

A man is standing in the corridor of a ten storey building and looking at a tall tree in front of the building he sees the top of the tree at an angle of depression 30degree if the tree is 200metre tall and the man's eyes are 300metre above the ground calculate the angle of depression of the foot of the tree as seen by the man

Answer 1

tan30=500/x

1/root3

Answer 2

since the top of the tree is 100m down, and tan30° = 1/√3,

the tree is 100√3 meters from the building.

So if the angle to the foot of the tree is x, then
tanx = 300 / 100√3 = 3/√3 = √3
x = 60°

Answer 3

Well, it seems like our man has a bit of a "high" perspective, doesn't he? Let's see what we can do here.

First, we have the angle of depression, which is the angle between the line of sight and the horizontal. In this case, it's 30 degrees.

Now, we know that the height of the tree is 200 meters and the man's eyes are 300 meters above the ground. So, the total distance between the man's eyes and the top of the tree is 200 + 300 = 500 meters.

Since the man is looking down towards the tree, the angle of depression of the top of the tree is 30 degrees. But, to find the angle of depression of the foot of the tree, we need to consider the distance between the man and the tree.

So, using a little bit of trigonometry, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 200 meters (height of the tree) and the adjacent side is the distance between the man and the tree (let's call it x).

Therefore, tan(30 degrees) = 200 / x

Simplifying this equation, we have:

x = 200 / tan(30 degrees)

x = 200 / (1 / √3)

x = 200 * √3

x = 200√3 meters

Now, we have the distance between the man and the tree, which is 200√3 meters. We can use this information to find the angle of depression of the foot of the tree.

The tangent of an angle is still equal to the opposite side divided by the adjacent side. In this case, the opposite side is 200 meters (height of the tree) and the adjacent side is 200√3 meters (the distance between the man and the tree).

So, the angle of depression of the foot of the tree can be calculated as:

tan(angle) = 200 / (200√3)

tan(angle) = 1 / √3

Angle = arctan(1 / √3)

Now, if you'll excuse the pun, let's "root" for the result!

Angle = arctan(1 / √3) = 30 degrees

So, the angle of depression of the foot of the tree, as seen by the man, is also 30 degrees.

I hope this "treeted" your question appropriately!

Answer 4

To solve this problem, we can use the concept of trigonometry and the properties of right-angled triangles.

Let's break down the information given:

1. The height of the tree is 200 meters.
2. The man's eye level is 300 meters above the ground.
3. The angle of depression to the top of the tree is 30 degrees.

Now, let's find the height from the man's eye level to the top of the tree:

We have a right triangle where the length from the man's eye level to the top of the tree is the opposite side, and the distance from the man to the building is the adjacent side. The angle between these two sides is 30 degrees.

Using trigonometry, we can use the tangent function to find the length from the man to the building:

tan(30 degrees) = opposite / adjacent
tan(30 degrees) = 200 meters / adjacent

Now, let's find the adjacent side:

adjacent = 200 meters / tan(30 degrees)
adjacent = 200 meters / 0.5774
adjacent ≈ 346.41 meters

Now, we have the opposite side (the height from the man's eye level to the top of the tree) and the adjacent side (the distance from the man to the building). We can find the hypotenuse of this right triangle:

hypotenuse = sqrt((opposite^2) + (adjacent^2))
hypotenuse = sqrt((200 meters)^2 + (346.41 meters)^2)
hypotenuse = sqrt(40000 meters^2 + 120000 meters^2)
hypotenuse = sqrt(160000 meters^2)
hypotenuse ≈ 400 meters

Now, to find the angle of depression to the foot of the tree:

We have a right triangle where the length from the man's eye level to the foot of the tree is the opposite side, and the distance from the man to the building (which we just found to be approximately 346.41 meters) is the adjacent side.

Using trigonometry, we can use the tangent function to find the angle:

tan(angle) = opposite / adjacent

Now, let's substitute the values:

tan(angle) = 300 meters / 346.41 meters

To find the value of angle, we can use the arctan function:

angle = arctan(300 meters / 346.41 meters)
angle ≈ 42.63 degrees

Therefore, the angle of depression to the foot of the tree as seen by the man is approximately 42.63 degrees.

Answer 5

To calculate the angle of depression of the foot of the tree as seen by the man, we can use trigonometry.

First, let's draw a diagram to visualize the situation:

```
T /|
/ |
200m / |
/ | 300m
/ α |
/____|

```

In this diagram, the man is standing in the corridor of the ten-story building (300 meters above the ground) and looking at a tall tree (200 meters tall).

We know that the man sees the top of the tree at an angle of depression of 30 degrees. Let's call this angle α.

Now, we need to find the angle of depression of the foot of the tree, which we'll call angle β.

To find β, we can use the fact that the sum of the angles in a triangle is 180 degrees.

In triangle TAB, where T is the top of the tree, A is the foot of the tree, and B is the point where the man is standing, we have angle α (30 degrees) at vertex A and angle β at vertex B.

Therefore, we can find β using the equation:

β = 180 degrees - α.

Substituting the given values:

β = 180 degrees - 30 degrees.

β = 150 degrees.

So, the angle of depression of the foot of the tree as seen by the man is 150 degrees.