From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57°, as shown below. If the height of the balloon is 15 miles, what is the distance between the radio antenna and the library?

Question

i<3mybaby · Answer

A.	23.1 miles
	B.	12.7 miles
	C.	8.2 miles
	D.	11.6 miles

anonymous · Answer

Since we have a right triangle we can apply the pythagorean theorem as well as SOH CAH TOA

anonymous · Answer

Using the angle and side that you know which might you use?

i<3mybaby · Answer

Im thinking sin or tan

anonymous · Answer

Well if we solve for the missing angle we can use any one of them but yes one of those is correct, from the picture we see that we have 1 angle and the opposite side is the base and that the hypotenuse is missing but we have the adjacent side to that angle.

anonymous · Answer

So knowing we do not have the hypotenuse we see which 1 we use

i<3mybaby · Answer

tan

i<3mybaby · Answer

@dan815 
@jdoe0001

jdoe0001 · Answer

|dw:1403395060772:dw|  keep in mind that, for an angle, the "opposite" side is the side that it's "facing it off"

and the "adjacent" side is the one that touches it, usually the smaller one side that touches it

$\bf tan(\theta)=\cfrac{opposite\ side}{adjacent\ side}\implies adjacent\ side\cdot tan(\theta)=opposite\ side
\ \quad \
tan(57^o)=\cfrac{{\color{brown}{ x}}}{15}\implies 15\cdot tan(57^o)={\color{brown}{ x}}$

i<3mybaby · Answer

23.09 making it 23.1

jdoe0001 · Answer

yeap, rounded up is 23.1