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

is my answer correct

Answer 1

let's see. we can also say that
h cot47° + h cot36° = 125
h = 54.14

So, what's wrong with your solution?
The law of sines only works when applied to the same triangle.

Answer 2

so my answer should be:
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 3

d1 + d2 = 125 m.
Tan47 = h/d1; h = d1*Tan 47 = (125-d2)Tan 47.
Tan36 = h/d2; h = d2*Tan36.

h = (125-d2)*Tan 47 = d2*Tan 36.
(125-d2)*Tan 47 = d2*Tan 36,
d2 = 74.4 m,
d1 = 125-74.4 = 50.6 m.

h = d2*Tan 36 = 74.4*Tan 36 = 54.1 m.

Answer 4

thanks henry2,