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?

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): You can put this solution on YOUR website!
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
RELATED QUESTIONS
The speed of the current in a river is 5 miles per hour. A boat leaves a dock on the... (answered by lynnlo,Finavon)

A boat leaves a shipping dock and travels 72 miles due west then 99 miles due north.... (answered by josmiceli)

Hi, I have a math problem I don't know how to do, it's: A boat leaves from a dock,... (answered by solver91311)

I don't understand how to solve these two question. Can someone please explain in detail? (answered by Alan3354)

a boat went 15 miles downstream in 1 hour and then returned to its dock in 5/3 hours. if... (answered by josmiceli)

A boat leaves a dock and travels at the rate of 36 kilometers per hour. Twenty minutes... (answered by greenestamps)

At 1:30pm Tom leaves in his boat from a dock and heads south at a rate of 25 miles per... (answered by alicealc)

a boat can travel 20 km per hour. the current in the river flows at 5 km per hour. so... (answered by ewatrrr)