Aboat is 400 feet away from one dock and 300 feet away from another dock the angle between the two paths is 45. what is the approximate distance between the docks ?

Answer is 283 feet!

Step-by-step explanation:

283.363 feet

Step-by-step 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

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative