A golfer hits a tee shot on a 285m long straight golf hole. The ball is hooked (hit at an angle) 14degree to the left. The ball lands 183m from the tee. How far is the ball from the hole?
using the law of cosines,
d^2 = 285^2 + 183^2 - 2(285)(183)cos14°
d = 116.2m
Thank you Steve
To find the distance of the ball from the hole, we can use trigonometry.
First, let's find the horizontal distance covered by the ball. This is equal to the distance the ball landed minus the distance it would have covered if hit straight.
The horizontal distance covered by the ball is given by:
Horizontal distance = Distance landed * cos(angle)
Substituting the given values:
Horizontal distance = 183m * cos(14 degrees)
Calculating the horizontal distance:
Horizontal distance = 183m * 0.9703 = 177.7649m
Therefore, the ball is 177.7649m from the hole.
To determine how far the ball is from the hole, we can use the concept of a right triangle and apply some trigonometry. Let's break down the problem:
1. The straight golf hole is 285 meters long. This represents the hypotenuse of a right triangle.
2. The ball lands 183 meters from the tee. This represents the shorter side of the right triangle.
3. The golfer hit the ball at a 14-degree angle to the left, which forms the angle opposite the longer side of the right triangle.
To find the longer side (the distance the ball is from the hole):
1. Use the given angle of 14 degrees and the opposite side length of 183 meters to find the length of the adjacent side.
- We can use the trigonometric function "cosine" (cos) to solve this.
- The formula is: adjacent side length = opposite side length ÷ cosine(angle).
- In our case, adjacent side length = 183 ÷ cos(14).
2. Once we have the adjacent side length, we can subtract it from the total length of the hole (285 meters) to determine the distance the ball is from the hole.
- Distance from the hole = total length of the hole - adjacent side length.
Now, let's calculate:
Using a calculator or a programming language, we can find cos(14 degrees) ≈ 0.9703.
1. adjacent side length ≈ 183 ÷ 0.9703 ≈ 188.481 meters.
2. Distance from the hole ≈ 285 - 188.481 ≈ 96.519 meters.
Therefore, the ball is approximately 96.519 meters from the hole.