A golfer hits a tee shot on a 325 m long straight golf hole. The ball is hooked (hit at an angle of 18 degrees to the left. The ball lands 185 m from the tee. How far is the ball from the hole ?
Did you draw your triangle?
Did you review the law of cosines?
x^2 = 185^2 + 325^2 - 2*185*325*cos18°
I just finished the calculations and it gave me an answer of 160 m
To find the distance from the ball to the hole, we need to calculate the horizontal distance and vertical distance separately and then find the hypotenuse using the Pythagorean theorem.
1. Calculate the horizontal distance:
The ball was hit at an angle of 18 degrees to the left, which means it deviated from a straight line by 18 degrees. To find the horizontal distance, we use the cosine function: cos(18) = adjacent / hypotenuse.
adjacent = hypotenuse * cos(18)
adjacent = 185 m * cos(18)
2. Calculate the vertical distance:
The vertical distance is given by the height difference between the tee and the landing spot of the ball. Since there is no mention of the height, we can assume the tee and landing spot are at the same height. Therefore, the vertical distance is zero.
3. Use the Pythagorean theorem to find the distance from the ball to the hole:
The horizontal distance (adjacent) is already calculated, and the vertical distance (opposite) is zero.
Let the distance from the ball to the hole be x.
x^2 = adjacent^2 + opposite^2
x^2 = (185 m * cos(18))^2 + 0^2
Finally, solve for x, which represents the distance of the ball from the hole.
To find the distance from the hole, we need to use trigonometry.
Since the ball was hooked to the left, it veered off from the straight path towards the hole. We can consider the straight path towards the hole as the hypotenuse of a right triangle. The distance the ball traveled along the straight path is the adjacent side, and the distance it veered off to the left is the opposite side.
Given that the ball was hit at an angle of 18 degrees to the left, we can use the trigonometric function cosine (cos) to find the distance along the straight path:
Adjacent side = Hypotenuse x cosine(angle)
In this case:
Hypotenuse = 325 m
Angle = 18 degrees
Adjacent side = 325 x cos(18)
To find the distance from the hole, we need to subtract the distance the ball traveled along the straight path from the total length of the hole:
Distance from the hole = Total distance - Distance along the straight path
Total distance = 325 m
Distance along the straight path = 325 x cos(18)
Distance from the hole = 325 - (325 x cos(18))
Now we can calculate the distance from the hole using this formula.