A hockey player skates down the ice at an angle of 34° to a line crossing the width of the rink. If he skates 14 m, how far has he travelled down the length of the ice toward the goal?
your use of the words "down" is confusing.
I think you mean the skate is skating at an angle 34deg to the width dimension, and you want to know the distance perpendicular to the width.
sin34=distance/14
14 *sin34= distance If I understood you correctly.
To find how far the hockey player has traveled down the length of the ice toward the goal, we need to calculate the component of the distance that is in the desired direction.
First, let's visualize the problem. Draw a diagram of a rink with a hockey player skating at an angle of 34°. Label the length of the ice as "L" and the width as "W".
The distance the player has traveled down the length of the ice can be found using trigonometry. We can use the sine function, as it relates the opposite side of a right triangle to the hypotenuse.
In this case, the length of the ice (L) is the hypotenuse, and the distance the player has traveled down the length is the opposite side. The angle of 34° is the angle between the line crossing the width of the rink (adjacent side) and the hypotenuse.
Using the formula for the sine function:
sin(angle) = opposite / hypotenuse
We have:
sin(34°) = opposite / L
Now, we can rearrange the equation to solve for the opposite side:
opposite = sin(34°) * L
Substituting the given length of 14 m for L, we can calculate the distance the player has traveled down the length of the ice toward the goal:
opposite = sin(34°) * 14 m
Using a calculator, we find that sin(34°) is approximately 0.559.
opposite = 0.559 * 14 m
opposite ≈ 7.826 m
Therefore, the hockey player has traveled approximately 7.826 meters down the length of the ice toward the goal.