Question

Phoebe and Holden are on opposite sides of a tall tree, 125 m apart. the angles of elevation from each top of the tree are 47 degrees and 36 degrees. what is the height of the tree?

My Answer:
The top angle will be = 180 - (47 + 36) = 97°
then we use the sine law:
(height of tree / sin 47) = (Base / sin 97)
height of tree = (125 x sin 47) / sin 97 = 92.1 m

or is this the answer:
tan 47 = h/x
tan 36 = h/(125-x)
x*tan47 = 125*tan36-x*tan36
x = 125*tan36/[tan47+tan36]
x = 50.485 m
h = 54.138 m

Answer 1

ooblek has not been on line since about 8:30, so I will answer

Your second solution is correct
Your answer using the sine law is invalid since you did not stay within the same triangle
You could have done this:
Let the top of the tree be T
PT/sin36 = 125/sin97
PT = 125sin36/sin97 = 74.0249..

now to the small right-angled triangle ....
sin 47 = h/PT
h = PTsin47 = 54.138, just like the answer to your second method

Answer 2

thanks Reiny