A soccer ball is placed 12 ft away from a goal post that measures 8ft high. You kick the ball and it hits the crossbar at the top of the goal. What was the angle of elevation of your kick?
tanθ = 8/12
roughly. θ actually needs to be slightly more, because the ball falls some due to gravity. But, a little investigation should convince you that the discrepancy caused by gravity can be eliminated because of the ball's diameter, given proper conditions.
To find the angle of elevation of your kick, we can use trigonometry. The angle of elevation is the angle between the ground and the line of sight from the kicker's eye to the highest point reached by the ball, which in this case is the top of the goal post.
First, we need to determine the horizontal distance from the kicker to the goal post. In this case, the soccer ball is placed 12 ft away from the goal post, so the horizontal distance is 12 ft.
Next, we need to determine the vertical distance from the ground to the top of the goal post. The goal post measures 8 ft high, which gives us the vertical distance.
Using these values, we can set up the tangent function, which is defined as the ratio of the opposite side to the adjacent side:
tan(angle) = opposite / adjacent.
In this case, the opposite side is the vertical distance (8 ft) and the adjacent side is the horizontal distance (12 ft).
tan(angle) = 8 ft / 12 ft.
To find the angle, we take the inverse tangent of both sides of the equation:
angle = arctan(8 ft / 12 ft).
Using a calculator, we can find the arctan of the fraction, which is approximately 33.7 degrees.
Therefore, the angle of elevation of your kick is approximately 33.7 degrees.