Question

the 2018 world cup broke the record for the most penalty kicks in a tournament. for a penalty kick, the ball is placed 38 feet from the goal line and the goal is 10 feet tall. the ball needs to be kicked between 12° and what angle to make it into the goal?
answer x = degrees
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Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the opposite side to the angle \( x \) is the height of the goal (10 feet) and the adjacent side is the distance from the ball to the goal line (38 feet). So we use the tangent function, which is \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \).

Step2: Calculate the angle

We know the opposite side \( o = 10 \) and adjacent side \( a = 38 \). So \( \tan(x)=\frac{10}{38}\approx0.2632 \). To find \( x \), we take the arctangent (inverse tangent) of 0.2632: \( x=\arctan(0.2632) \). Using a calculator, \( \arctan(0.2632)\approx14.7^\circ \) (rounded to one decimal place).

Answer:

\( 14.7 \) (or other reasonable approximation based on calculator precision)