The sun cast a 5.45 foot shadow of a person. The angle of elevation is 50 degrees.what is the approximate height of the person? Round to the nearest tenth

Question

please include all work so I can understand it. Thank you for the help it is much appreciated 

Answer 1

Here is a picture I drew with numbered steps, I hope this helps:

 

http://i.imgur.com/m0THJNE.jpg

 

Essentially this is a right triangle with one of the angles given.  We want to find one side.  There are multiple ways to do this, but the easiest one that you can immediately do with the information given is use the tangent function.  Tangent is sine divided by cosine, but simplified it ends up being opposite divided by adjacent.  We have the adjacent side and the angle, so we set up the equation:

 

tan 50 = (x / 5.45)

Cross multiply and get:

x = (tan 50)(5.45)

Use your calculator to get:

x = 6.495...

Round to the nearest tenth:

x = 6.5

 

I hope this helps!