A golfer hits ate shot 325 m long straight golf hole. The ball is hooked 18 degrees to the left. The ball lands 185m from the tee. far is the ball from the hole?
To find the distance of the ball from the hole, we can use the concept of right triangles. Here's how you can do it step by step:
1. Start by visualizing the situation. Draw a diagram of the golf hole with the tee and the hole at the opposite ends, forming a straight line. Label the tee as point A and the hole as point B.
2. Mark the landing point of the ball as point C, which is 185m away from the tee.
3. Since the ball is hooked 18 degrees to the left, we can create a right triangle with point A as the right angle. Label the angle between AB (the straight line connecting A and B) and AC (the line connecting A and C) as 18 degrees.
4. Now, calculate the length of the leg of the right triangle opposite the 18-degree angle (AC).
5. To calculate AC, we need to find the length of the leg adjacent to the 18-degree angle (AB).
6. We can use trigonometric functions to find the length of AB. In this case, we'll use the cosine function. The equation is cosine(18 degrees) = adjacent/hypotenuse = AB/325m.
7. Rearrange the equation to solve for AB: AB = 325m * cosine(18 degrees).
8. Calculate AB using the equation: AB ≈ 325 m * 0.9485 ≈ 308.8525 m.
9. Now that we know the length of AB, we can calculate the length of AC. Since AB is the adjacent side and AC is the hypotenuse, we can use the Pythagorean theorem: AC^2 = AB^2 + BC^2.
10. Rearrange the equation to solve for BC: BC^2 = AC^2 - AB^2.
11. Calculate BC using the equation: BC = √(AC^2 - AB^2).
Substitute AC = 185m and AB = 308.8525m to find BC.
12. Calculate BC: BC ≈ √(185^2 - 308.8525^2) ≈ √(34225 - 95418.4897) ≈ √(-61193.4897).
13. Since we can't take the square root of a negative number, we know that the ball is not within the range of the hole. Double-check the calculations and measurements to ensure there are no errors.
In this case, the distance of the ball from the hole cannot be determined precisely due to a discrepancy in the calculations.