The Distance Dilemma

I've been walking quite a while. How much further do I need to go to get to that store?

Excuse me sir. I need help finding how far I am from the store over there.

Sure thing. I built that store. When I built it, I measured the distance and angle to the bottom of that awning from the end of that bench where you are now.

Clothing Store

Clothing Store

Clothing Store

From what I remember, the distance between you, and the awning of the store is 97ft with an 11 degree angle of elevation. The distance between the bottom of the awning and the base pf the door should be 9ft, with a 76 degree angle in between those sides. That's all I can help you with, sorry.

97ft

11°

9ft

Clothing Store

97ft

11°

9ft

76°

Clothing Store

97ft

11°

9ft

76°

x

This is easy, I know Law of Sines! With this information, I can set up the equation sin(11)/9 = sin(76)/x. Cross multiply to get xsin(11) = 9sin(76). Divide sin (11) on both sides to get x = 9sin(76)/sin(11), which results in an answer of about 45.77

Clothing Store

97ft

11°

9ft

Clothing Store

97ft

11°

9ft

76°

45.77ft

That is very impressive! So... now that you know how far you are from the store are you going to walk there?

Yes I will. Discussing this has given me enough time to actually catch my breath.

The End