The exact distance and direction that Patrick is from Johnny is; 177.81 ft and 215.52°
Let the distance of Johnny to Patrick be x.
The angle opposite x would be; (90 - 50) + 90 + 30 = 160°
We will therefore use the cosine rule to find x;
X² = A² + B² - 2ABcosx
Where;
A and B are the distance of Johnny to Rob and Rob to Patrick respectively. Thus;
X² = 130² + 50² - 2(130)(50)cos160
X²= 16900 + 2500 + 12216.004
X² = 31616.004
X = 177.81 ft
To get the direction "y" we will use sine rule;
50/siny = 177.809/sin160
50/siny = 177.809/0.342
50/siny = 519.9094
Siny = 50/519.904
Siny = 0.09617
y = sin⁻¹(0.09617)
y = 5.52°
The bearing of Patrick from Johnny is;
5.52 + 30 + 180 = 215.52°
Read more about Trigonometric Ratios at; https://brainly.com/question/24349828
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