A man travels at 42 degrees northwest, and ends up 8.5 miles west of his starting point. How far did he travel?

The man traveled 12.70 miles.

Step-by-step explanation:

We can find the distance traveled by the man knowing:

: the distance at the west = 8.5 miles

: the northwest angle = 42°

Then by using the following trigonometric identity we have:

Therefore, the man traveled 12.70 miles.

I hope it helps you!                                    

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.