A flag pole sits on the front lawn of a school, 6.6 m from the front door. The angle of elevation from the base of the school to the top of the pole is 38°. Determine the height of the flagpole, to the nearest tenth of a metre.
Just a simple case of
tan38 = h/6.6
h = 6.6tan38°
= ....
To determine the height of the flagpole, we can use trigonometry and the given information.
First, let's sketch a diagram to visualize the problem. Place the school's front door at the origin of a coordinate system, and label the flagpole as a vertical line extending upward from a point on the x-axis, 6.6 meters away from the origin. We can label this point as (6.6, 0). Now draw a line from the origin to the top of the flagpole, creating a right triangle.
The angle of elevation from the base of the school to the top of the pole is 38°, so we can label this angle as θ. The line from the base of the school to the top of the flagpole represents the opposite side of the right triangle, and the vertical line (flagpole) represents the adjacent side.
We need to find the height of the flagpole, which represents the opposite side of the triangle. To do this, we'll use the trigonometric function tangent (tan). The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
In this case, tan(θ) = opposite / adjacent
tan(38°) = opposite / 6.6 m
opposite = 6.6 m * tan(38°)
Using a calculator, we can find that tan(38°) ≈ 0.7813. So, the opposite side (height of the flagpole) is approximately:
opposite = 6.6 m * 0.7813 ≈ 5.142 m
Therefore, the height of the flagpole is approximately 5.1 meters (rounded to the nearest tenth of a meter).