We are given that a hockey player takes a shot 20 feet away from a 5-foot goal and that the puck travels at a 15^(∘) angle of elevation toward the center of the goal. Let h be the height of the puck when it reaches the goal. Let's sketch a diagram describing this situation.
Since the figure is a right triangle, we can use one of the trigonometric ratios to evaluate the value of h. Let's recall that the tangent of ∠A is the ratio of the leg opposite ∠A to the leg adjacent ∠A. Using this definition, we can create an equation for tan 15^(∘).
tan 15^(∘)=h/20
Let's solve the above equation.
The height of the puck is approximately 5.4 feet. Notice that the goal has a height of 5 feet which is less than the height that the puck reached. Therefore, the player will not score.
