The sun casts the shadow of a 10-foot tree on the ground with an angle of elevation of 33 degrees. If you are standing on the top of the shadow, approximately how far are you from the tree?

you are at a distance of 15.4 feet from the tree

Step-by-step explanation:

with the data they give us we can imagine a rectangular triangle, where the legs are the floor and the tree and the hypotenuse is the distance between the tip of the tree and the end of the shadow

we have to that the angle of elevation is 33 degrees

at the angle we will call it α

and the height of the tree we will call it opposite since it does not touch the angle

the distance we want to know we will call it adjacent

we see that it has (angle, adjacent, opposite)

well to start we have to know the relationship between angles, legas and the hypotenuse

a: adjacent

o: opposite

h: hypotenuse

sin α = o/h

cos α = a/h

tan α = o/a

it's the tangent

tan α = o/a

we replace the values and solve

tan α = o/a

tan 33 = 10/a

a = 10 / tan 33

a = 15.4