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.
To find the height of the flagpole, we can use the concept of trigonometry. Let's break down the information given:
- The angle of elevation from observer 0 to the bottom of the flagpole is 36 degrees.
- The angle of elevation from observer 0 to the top of the flagpole is 38 degrees.
- The distance from observer 0 to the flagpole is 200 meters (base).
From these details, we can draw a right-angled triangle, where the height of the flagpole is the unknown side that we need to find. The base of the triangle is the distance from the observer to the flagpole.
Using the trigonometric function "tangent," we can relate the angle of elevation to the sides of the triangle. The tangent of an angle is the ratio of the opposite side to the adjacent side.
Let's designate the height of the flagpole as 'h.' Now, we can set up two trigonometric equations by applying the tangent function to the angles of elevation:
1) tan(36 degrees) = h / 200
2) tan(38 degrees) = (h + x) / 200, where 'x' is the segment between the top of the flagpole and observer 0.
Since the base of the triangle is the same for both equations, we can set them equal to each other:
h / 200 = (h + x) / 200
Now, we can solve this equation to find 'h.' By rearranging and canceling the common factor of 200:
h = h + x
x = h - h = 0
Therefore, the segment 'x' is zero since there is no horizontal difference between the top and bottom of the flagpole as observed from observer 0.
Substituting x = 0 into equation (2):
tan(38 degrees) = h / 200
Now, we can solve for 'h.' Multiply both sides of the equation by 200:
200 * tan(38 degrees) = h
Using a calculator, we find:
h ≈ 199.37 meters
Therefore, the height of the flagpole is approximately 199.37 meters.