Question

A tree 19 feet tall casts a shadow which forms an angle of 49 degrees with the ground. How long is the shadow?

Answer 1

`x~~16.5164591425`

Explanation:

Let's visualize our situation here.
So we have:

Remember the Soh Cah Toa.
(Sin=>opposite/hypotenuse)
(Cos=>adjacent/hypotenuse)
(Tan=>opposite/adjacent)

Looking at our illustration, we see that the side with the length 19 feet is opposite to our given angle(49 degrees.)

Since the shadow(bottom side) is adjacent to the angle, we use tangent for our problem.
`19/x=tan49/1` We isolate `x`:
`19=xtan49`
`19/tan49=x`
`x~~16.5164591425`
That is our answer!