I can't figure this out.
A famous golfer tees off on a long, straight 459 yard par 4 and slices his drive 10 degrees to the right of the line from tee to the hole. If the drive went 288 yards, how many yards will the golfer's second shot have to be to reach the hole?
just use the law of cosines:
x^2 = 459^2 + 288^2 - 2*459*288 cos 10°
To solve this problem, we can use trigonometry. Let's break it down into steps:
Step 1: Find the horizontal distance covered by the drive
The golfer's drive went 288 yards, with a slice 10 degrees to the right of the line from the tee to the hole. This means the golfer's drive covered the adjacent side of a right triangle. We can use cosine to find the horizontal distance covered by the drive.
Adjacent side = hypotenuse * cosine(angle)
Adjacent side = 288 yards * cosine(10 degrees)
Adjacent side ≈ 288 yards * 0.985
Adjacent side ≈ 283.68 yards (rounded to the nearest yard)
Step 2: Find the remaining distance to the hole
Since the golfer teed off on a 459 yard par 4, we can subtract the distance covered by the drive from the total distance to find the remaining distance to the hole.
Remaining distance = Total distance - Distance covered by the drive
Remaining distance = 459 yards - 283.68 yards
Remaining distance ≈ 175 yards (rounded to the nearest yard)
Therefore, the golfer's second shot will need to travel approximately 175 yards to reach the hole.
To find the distance the golfer's second shot will have to be to reach the hole, we can break down the problem by using trigonometry.
Step 1: Draw a diagram to visualize the situation. Draw a straight line to represent the path from the tee to the hole. Mark a point to represent the starting position of the drive. Draw a line at a 10-degree angle from the line representing the path from the tee to the hole to represent the slice. Measure the length of this line to represent the distance traveled by the drive.
Step 2: Use trigonometry to find the horizontal distance traveled by the drive. Since we know the angle and the distance traveled, we can use the trigonometric function cosine to find the horizontal distance. The formula is:
Horizontal Distance = Drive distance * cosine(angle)
In this case, the drive distance is 288 yards and the angle is 10 degrees. Substituting these values into the formula:
Horizontal Distance = 288 * cosine(10 degrees)
Step 3: Calculate the horizontal distance using a scientific calculator or by using a calculator app on your computer or smartphone.
Horizontal Distance ≈ 281.87 yards (rounded to two decimal places)
Step 4: Determine the remaining distance to the hole. Since the par 4 is 459 yards long, to find the remaining distance after the drive, subtract the horizontal distance from the total length of the hole:
Remaining Distance = Total length of the hole - Horizontal Distance
Remaining Distance = 459 yards - 281.87 yards
Step 5: Calculate the remaining distance to the hole.
Remaining Distance ≈ 177.13 yards (rounded to two decimal places)
Therefore, the golfer's second shot will have to be approximately 177.13 yards to reach the hole.