What is the height of the tree?

Question

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60 degrees, and from a second position L= 30 feet farther along this path it is B=50°. What is the height of the​ tree?

Answer 1

I'm using trig.

side a =30'

angle α=10°

β=50°

γ=120°

a/sinα=b/sinβ=c/sinγ

30/sin10=172.763...=c/sin120

c=172.763*.866...=149.617...

Now we're working on a rt triangle.

angle α=40°

β=50°

γ=90°

side c=149.617...

We want side b. See above formula.

c/sinγ=149.617 (sin of a rt >=1)

=b/sinβ=b/.766...*149.617...=114.613...ft

I drew/labeled the triangles.