Question

The distance between two locations, A and B, is calculated using a third location C at a distance of 15 miles from location B. If B = 105° and C = 20°, what is the distance, to the nearest tenth of a mile, between locations A and B?


A 42.4 miles
B 35.9 miles
C 6.3 miles
D 5.3 miles

Answer 1

So I made a triangle:



To solve for X, we can fall back on our useful little term, cosine. Here. Lemme show ya how it works.

Cosine (of some given angle) = Adjacent Side / Hypotenuse. We know this. Soooooo, let's fill in teh blanks.

Cos (20) = (15) / (x).

This is the same thing as saying: (x) = ( (15) / (cos)(20) ).

When you solve dat out, you get: x = 15.96. So now we've solved for X. Pretty easy to solve for Y now, right? Right. Just use the Pythagorean Theorem. Fill in the X-side on my little triangle diagram to help you visualize what's happening a bit better.

The longest side of our constructed triangle is equal to 15.96, so:

(15.96)^2 = (y)^2 + (15)^2

We'll solve that out.

(15.96)^2 = (y)^2 + (15)^2 ...Becomes:
(254.81) = (y)^2 + (225) ...Becomes:
(y)^2 = 29.81 ...Becomes:
(y) = 5.46. This value here represents the distance from Point A to Point B.

The closest choice to this answer is: D.