From an observer 0, the angles of elevation to the bottom and top of the flag pole are 36 degree and 38 degree respectively. The base is 200m. Find the height of the flag pole.
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To find the height of the flagpole, we can use the concept of trigonometry. Since we have the angles of elevation, we can use the tangent function to solve for the height.
Let's consider the triangle formed by the observer (point O), the bottom of the flagpole (point A), and the top of the flagpole (point B). The base of the triangle is given as 200m.
First, let's find the height from the observer to the bottom of the flagpole (OA).
Using the tangent function, we have:
tan(36°) = OA / 200
Rearranging this equation to solve for OA, we get:
OA = 200 * tan(36°)
OA ≈ 200 * 0.7265
OA ≈ 145.3m
Next, let's find the height from the observer to the top of the flagpole (OB).
Using the tangent function, we have:
tan(38°) = OB / 200
Rearranging this equation to solve for OB, we get:
OB = 200 * tan(38°)
OB ≈ 200 * 0.7813
OB ≈ 156.3m
Finally, to find the height of the flagpole (AB), we subtract the height from the observer to the bottom of the flagpole (OA) from the height from the observer to the top of the flagpole (OB).
AB = OB - OA
AB = 156.3 - 145.3
AB ≈ 11m
Therefore, the height of the flagpole is approximately 11 meters.
To find the height of the flagpole, we can use the concept of trigonometry, specifically the tangent function.
Let's denote the height of the flagpole as "h". From the given information, we have two angles: the angle of elevation to the bottom of the flagpole (36 degrees) and the angle of elevation to the top of the flagpole (38 degrees).
From observer 0, imagine a right-angled triangle where the observer, the bottom of the flagpole, and the top of the flagpole form the three points of the triangle. The base of this triangle is given as 200m.
Now, we can use the tangent function to relate the angles and the height of the flagpole, as follows:
For the angle of 36 degrees:
tan(36) = h / 200
For the angle of 38 degrees:
tan(38) = (h + x) / 200
Here, "x" represents the distance from the bottom of the flagpole to the observer.
We can solve these two equations for the height "h" by equating them:
h / 200 = (h + x) / 200
By canceling out the common factor of 200, we get:
h = h + x
Subtracting "h" from both sides, we have:
0 = x
Therefore, x = 0. This suggests that the observer is standing right at the base of the flagpole (x = 0).
Now, substitute x = 0 into any of the initial equations to find the height "h":
tan(36) = h / 200
Rearranging the equation to solve for "h", we get:
h = tan(36) * 200
Using a calculator, evaluate the value of tan(36) ≈ 0.7265.
Therefore, the height of the flagpole is:
h ≈ 0.7265 * 200
h ≈ 145.3 meters
Hence, the height of the flagpole is approximately 145.3 meters.