SOLUTION: On at 550m hole, steve'a tee shoot goes 195m and is 21 degrees to the right of the direct path to the flag. The second shot flies 13 degrees to the right of the new direction tow
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Question 1168835: On at 550m hole, steve'a tee shoot goes 195m and is 21 degrees to the right of the direct path to the flag. The second shot flies 13 degrees to the right of the new direction toward the flag. but only travels 160m. How far is steve's golfball from the flag? show the steps of your solution and diagram
Answer by CPhill(2138) (Show Source): You can put this solution on YOUR website!
Absolutely! Let's break down this golf problem step-by-step.
**1. Diagram**
```
Flag (F)
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
(S2)--------------------(S1)
\ 13 degrees / 21 degrees
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
(T) Tee
```
* **T:** Tee point
* **S1:** Steve's first shot landing point
* **S2:** Steve's second shot landing point
* **F:** Flag
**2. Calculate the distance from Tee to S1**
* Distance (TS1) = 195m
* Angle from direct path = 21 degrees
**3. Calculate the distance from S1 to S2**
* Distance (S1S2) = 160m
* Angle from new direction = 13 degrees
**4. Calculate the distance from Tee to Flag**
* Distance (TF) = 550m
**5. Applying the Law of Cosines**
We need to find the distance from S2 to F (S2F). To do this, we need to find the angle between the line TS1 and the line S1S2.
* To find the angle between TS1 and S1S2, we need to add the two given angles. 21 degrees + 13 degrees = 34 degrees.
Now we can use the Law of Cosines to find the distance between the tee and the S2 point. We will call that distance TS2.
* TS2^2 = 195^2 + 160^2 - 2(195)(160)cos(34)
* TS2^2 = 38025 + 25600 - 62400(0.829)
* TS2^2 = 63625 - 51730
* TS2^2 = 11895
* TS2 = sqrt(11895) = 109.06
Now we need to find the angle between the direct path to the flag and the path from the tee to S2. We will call this angle A. We can use the law of sines to find this angle.
* 160/sin(A) = 109.06/sin(34)
* Sin(A) = 160*sin(34)/109.06
* Sin(A) = 0.814
* A = arcsin(0.814) = 54.5 degrees
Now we can calculate the angle between the direct path to the flag and the path from S2 to the flag. This angle will be 54.5 degrees.
Now we can calculate the distance from S2 to the flag using the law of cosines.
* S2F^2 = 550^2 + 109.06^2 - 2(550)(109.06)cos(54.5)
* S2F^2 = 302500 + 11894.08 - 120000(0.5807)
* S2F^2 = 314394.08 - 69684
* S2F^2 = 244710.08
* S2F = sqrt(244710.08) = 494.68
**6. Final Answer**
Steve's golf ball is approximately 494.68 meters from the flag.
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