A famous golfer tees off on a long, straight 472 yard par 4 and slices his drive 11 degrees to the right of the line from the tee to the hole. If the drive went 285 yards,how many yards will the golfer's second shot have to be to reach the hole?
To find out how many yards the golfer's second shot needs to be to reach the hole, we need to use some geometry.
First, let's break down the problem:
- The golfer sliced his drive 11 degrees to the right of the line from the tee to the hole.
- The drive went 285 yards in total.
- The total length of the hole is 472 yards.
- We need to determine the length of the golfer's second shot to reach the hole.
Now, let's look at the diagram below:
A 285yds
*-------------*---------*
/|<-11 degrees | \
/ | | x \
/ | ↓ \
T (tee) *--------------------------------------* H (hole)
472yds
In this diagram, T represents the tee and H represents the hole. The golfer's drive is represented by the arrow marked with the letter A. The angle of slicing is marked as 11 degrees. The distance from the tee to the golfer's drive is 285 yards, represented by the segment labeled "285yds." The total length of the hole is 472 yards.
Since we know that the golfer sliced his shot 11 degrees to the right, we can use trigonometry to find the horizontal distance (x) between the golfer's drive and the hole, which is the length we need to determine.
Using the trigonometric concept of cosine, we can set up the equation:
cos(angle) = adjacent/hypotenuse
Taking the cosine of 11 degrees, we have:
cos(11) = adjacent/285
Rearranging the equation to solve for adjacent, we get:
adjacent = cos(11) * 285
Using a calculator, we can find that the adjacent side is approximately 277.716 yards (rounded to three decimal places).
Now, to find the length of the golfer's second shot, we need to subtract the length of the golfer's drive (285 yards) from the adjacent side we just found:
x = 277.716 - 285
x is approximately -7.284 yards (rounded to three decimal places). The negative value tells us that the golfer's second shot would need to overlap with the previous shot for them to reach the hole.
In summary, the golfer's second shot would need to be approximately 7.284 yards short of the hole to reach it.