A man1.5m tall is 15m away from the building,24m high What is the angle of elevation of the top of the tree are 22° and 32° reprehensively. Find the height of the tree
We can solve this problem using trigonometry. Let's consider the triangle formed by the man, the tree, and the top of the building.
In this triangle, the angle of elevation of the top of the tree is 22° and the distance between the man and the building is 15m. The height of the building is given as 24m.
We can use the tangent function to find the height of the tree. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Let's call the height of the tree "h" since that's what we need to find.
From the given information, we can set up the following equation:
tan(22°) = h / 15
To solve for h, we multiply both sides of the equation by 15:
15 * tan(22°) = h
Using a calculator, we find that 15 * tan(22°) ≈ 5.62
So the height of the tree is approximately 5.62m.
Similarly, for the angle of elevation of 32°, we can set up the following equation:
tan(32°) = h / 15
To solve for h, we multiply both sides of the equation by 15:
15 * tan(32°) = h
Using a calculator, we find that 15 * tan(32°) ≈ 9.61
So the height of the tree is approximately 9.61m.
To find the height of the tree, we can use the concept of trigonometry.
Let's start by finding the distance between the man and the tree.
Using the angle of elevation of 22°, we can set up the following equation:
tan(22°) = height of the tree / distance to the tree
Since the height of the man is given as 1.5m and the distance to the building is given as 15m, we can calculate the horizontal distance from the man to the tree using the Pythagorean theorem:
(horizonal distance)^2 + (height of the man)^2 = (distance to the building)^2
(horizontal distance)^2 + 1.5^2 = 15^2
(horizontal distance)^2 + 2.25 = 225
(horizontal distance)^2 = 225 - 2.25
(horizontal distance)^2 = 222.75
(horizontal distance) ≈ √222.75
(horizontal distance) ≈ 14.92m
Now, we can calculate the height of the tree using the distance found:
tan(22°) = height of the tree / 14.92
height of the tree = tan(22°) * 14.92
height of the tree ≈ 5.69m
Therefore, the height of the tree is approximately 5.69 meters.
To find the height of the tree, we can use the tangent function and the given angles of elevation.
Let's start with the angle of elevation of 22°. We have a right triangle formed by the man (located at the base of the tree), the top of the tree, and the point on the ground directly below the top of the tree.
Using the tangent function, we can set up the equation: tan(22°) = height of the tree / distance from the man to the tree.
Since the distance from the man to the tree is given as 15m, we can rewrite the equation as: tan(22°) = height of the tree / 15m.
To solve for the height of the tree, we rearrange the equation: height of the tree = tan(22°) * 15m.
Using a calculator, we find that tan(22°) is approximately 0.4040.
Therefore, the height of the tree is: height of the tree = 0.4040 * 15m = 6.0606m (rounded to four decimal places).
Now, let's move on to the angle of elevation of 32°. We can use the same process as before.
Setting up the equation: tan(32°) = height of the tree / 15m.
Rearranging the equation: height of the tree = tan(32°) * 15m.
Using a calculator, we find that tan(32°) is approximately 0.6249.
Therefore, the height of the tree is: height of the tree = 0.6249 * 15m = 9.3735m (rounded to four decimal places).
To summarize, the height of the tree, based on the given angles of elevation, is approximately 6.0606m and 9.3735m, respectively.