Law of sines and cosines word problem

AC = 0.47 mi

BC = 0.51 mi

Step-by-step explanation:

Notice that we are in the case of an acute triangle for which we know two angles ( < A = 63 and < B = 56) and one side (AB = 0.5).

We can find the measure of the third angle using the property of addition of three internal angles of a triangle:

< A + < B + < C = 180

63 + 56 + < C = 180 degrees

< C = 180 - 63 - 56 = 61 degrees.

Now we use the law of sines to find the length of sides AC  and BC:

which can be rounded to two decimals as:

AC = 0.47mi

For side BC we use:

which can be rounded to two decimals as:

BC = 0.51 mi

14

step-by-step explanation:

a: 1/6, j: 1/4

step-by-step explanation: you are welcome