Answer:
Step-by-step explanation:
x ft from tree, the angle of elevation is 60°.
Altitude of nest is x√3.
x+200 ft from tree, the angle of elevation is 30°.
x+200 = (x√3)√3 = 3x
x = 100
One observer is 100 ft from tree. The other observer is 300 ft from tree.
Tangent formula is used to get the result. One observer is at 100 ft and another observer is at 300ft.
It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Two observers are 200 feet apart in line with a tree containing a bird's nest.
The angles of elevation to the bird's nest are 30° and 60°.
In ΔACD, we have
[tex]\rm tan 60 = \dfrac{200+x}{CD}\\\\C \ D \ \ = \dfrac{x+200}{\sqrt3}[/tex] ...1
In ΔBCD, we have
[tex]\rm tan 30= \dfrac{x}{CD}\\\\C \ D \ \ = x\sqrt3[/tex] ...1
From equation 1 and 2, we have
x = 100
One observer is at 100 ft and another observer is at 300ft.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
