Answer:
Height of helicopter above ground = 13.63 feet
Explanation:
See attached image to support explanation
B is the point vertically below where the helicopter is located
s is the distance from Sofie to B
d is the distance from Danika to B
We have
s + d = 100 ==> s = 100 -d
h is the height of the helicopter from the base
Both triangles are right triangles
For a right triangle,
tan x = Side opposite hypotenuse/Side adjacent to hypotenuse
where x is the angle between the side adjacent to the hypotenuse
Using this information for both triangles we get

Therefore
s (tan 10) = d ( tan 31)
But s = 100 -d:
(100-d) tan 10 = d ( tan 31)
100(tan 10) - d(tan 10) = d (tan 31)
Switch sides:
d (tan 31) = 100 (tan 10) - d( tan 10)
Add d (tan 10) to both sides:
d (tan 31) + d ·(tan 10) = 100(tan 10)
d(tan 31 + tan 10) = 100 (tan 10)

Using a calculator we can compute right side as

So
d = 22.6878
Plug this value of d into h = d sin 31 to get
h = d (tan 31)
h = 22.688 (0.6009)
h = 13.6322....
= 13.63 rounded to 2 decimal places
Height of helicopter above ground = 13.63 feet