A student can see a tower from the closet point of the soccer field at his high school. The edge of the soccer field is about 05 feet from the water tower and the water tower stands at a height of 51 feet. What is the angle of elevation from the student's feet?
We can use the tangent function to find the angle of elevation.
Let x be the height from the student's feet to the top of the tower.
The distance from the closet point on the soccer field to the tower is the hypotenuse of a right triangle with legs of x and 50.
Using the Pythagorean Theorem, we have:
x^2 + 50^2 = (50.5)^2
Simplifying:
x^2 + 2500 = 2550.25
x^2 = 50.25
x = 7.08
Now we can use the tangent function:
tan(theta) = opposite/adjacent = x/50.5
theta = arctan(x/50.5)
theta = arctan(7.08/50.5)
theta ≈ 8.11 degrees
Therefore, the angle of elevation from the student's feet is approximately 8.11 degrees.