Answer:283.363 feet
Explanation:
First we represent the problem with a diagram, which is what I have done in the picture I sent,
From the diagram I labeled the first dock as B, the second dock as A, you can choose to label it any letter you want, and the angle between the two sides as said is 45 degrees,
And from the question we are to find the distance between A and B, which I labeled x
The problem gives a triangle with two sides known, and the included angle between the two sides known too,
So we use the formula from the cosine rule
Note: cosine rule states that with sides a, b, and c of a triangle, if a and b are known and C is the included angle which is the angle between the sides a and b, c can be expressed as the formula below
c2 = a2 + b2 - 2abcosC
Note: c is not the same as C
From our diagram,
c = x
a = 300 feet
b = 400 feet
C = 45degrees
and we are to find x
Imputing the values and solving
c2 = (300)2 + (400)2 - 2(300)(400)cos45
After solving, we have
c2 = 80294.373
c = root(80294.373) = 283.363
c = x = distance between A and B = 283.363 feet