the height of a flagpole if a student stands 37 feet from it and determines the angle of elevation to be 34 degrees and her eyes are 5.3 feet from the ground.
assuming the angle is to the top of the pole, the height
h = 5.3 + 37 tan 34°
To find the height of the flagpole, we can use trigonometry, specifically the tangent function.
Let's label the height of the flagpole as "h" (what we want to find), the distance from the student to the flagpole as "d" (given as 37 feet), and the angle of elevation as "θ" (given as 34 degrees). The height of the student's eyes from the ground is given as 5.3 feet.
We can consider the right triangle formed by the student, the top of the flagpole, and a point on the ground directly below the top of the flagpole.
Using the tangent function, we have:
tan(θ) = h / d
First, let's convert the angle from degrees to radians:
θ_radians = θ * (π / 180)
Now we can substitute the known values into the equation:
tan(θ_radians) = h / d
tan(34 * (π / 180)) = h / 37
To solve for h, we multiply both sides of the equation by 37:
h = 37 * tan(34 * (π / 180))
Using a scientific calculator or calculator app, we can find the approximate value:
h ≈ 24.62 feet
So, the height of the flagpole is approximately 24.62 feet.