A football player is attempting a field goal. The angle formed by the player's position on the field and the line of sight to each upright is 33o. If the distances to the uprights are 7.5 m and 10.0 m, calculate the width of the uprights.
looks like cosine law ...
let the width between the uprights be x m
x^2= 7.5^2 + 10.0^2 - 2(10)(7.5)cos 33°
= .....
I will let you finish the arithmetic , ( I got 5.52m)
yes
A angle is formed on a football field
To solve this problem, we can use the tangent function, which relates the angle and the lengths of the sides of a right triangle. The tangent of an angle is equal to the opposite side divided by the adjacent side.
Let's assume that the width of the uprights is represented by x.
Now, let's analyze the problem statement. The player's position, the two uprights, and the line of sight to each upright form a right triangle. The two sides of the right triangle are the distances to the uprights (7.5 m and 10.0 m), and the angle between the player's position and the line of sight is 33 degrees.
Using the tangent function, we can set up the following equations:
tan(33 degrees) = x / 7.5 m
tan(33 degrees) = x / 10.0 m
To solve for x, we can rearrange the equations:
x = tan(33 degrees) * 7.5 m
x = tan(33 degrees) * 10.0 m
Now, let's plug in the values:
x = 0.6494 * 7.5 m
x ≈ 4.87 m
x = 0.6494 * 10.0 m
x ≈ 6.49 m
Therefore, the width of the uprights is approximately 4.87 m and 6.49 m.