SOLUTION: A boat leaves its dock and travels for 5 miles in the direction perpendicular to the shore, then makes a 48o turn and travels another 3 miles. How far is the boat from the dock?

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Question 249746: A boat leaves its dock and travels for 5 miles in the direction perpendicular to the shore, then
makes a 48o turn and travels another 3 miles. How far is the boat from the dock?
Answer by ankor@dixie-net.com(22740) (Show Source):
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A boat leaves its dock and travels for 5 miles in the direction perpendicular to the shore, then makes a 48 degree turn and travels another 3 miles.
How far is the boat from the dock?
:
Forms an oblique triangle
Interior angle (A): 180 - 48 = 132 degrees
b = 5 mi
c = 3 mi
a = dist from dock to boat (side opposite angle A)
:
Use the law of cosines
a^2 = b^2 + c^2 - 2bc(cos(A))
a^2 = 5^2 + 3^2 - 2(5*3)cos(132)
a^2 = 25 + 9 - 30*-.66913
a^2 = 34 - (-20.07)
a^2 = 54.07392
a =
a = 7.3535 mi from the dock