Aboat is 400 feet away from one dock and 500 feet away from another dock.
the angle between the two paths is 45°. what is the approximate distance
between the docks?
o
a. 695 feet
o
o
o
b. 540 feet
c. 166 feet
d. 357 feet

The approximate distance  between the docks is 356.59 feet approximately.

Solution:

Given, A boat is 400 feet away from one dock and 500 feet away from another dock.  

The angle between the two paths is 45°.  

Now, Let d be the distance between the docks, which forms a third leg of a triangle for which the angle opposite it has measure 45 degrees.  

The other two legs have lengths 400 ft and 500 ft.

So, let us use the law of cosines:

where a, b, c are sides of triangle and C is angle opposite to side c.

Here in our problem, c = d, a = 400, b = 500 and C = 45

Hence, the distance between two docks is 356.59 feet approximately.

the answer is  

a.

4,624π mm2

step-by-step explanation: