Answer:
D. [tex]tan(30^\circ+45^\circ)[/tex] is the correct answer.
Step-by-step explanation:
The given situation can be represented as a figure attached in answer area.
B is the base of tree.
C is the base of wires.
A and D are the end of 2 wires supporting the tree.
[tex]\angle DCB =45^\circ\\\angle ACB =75^\circ\\[/tex]
Here, we need to find the Height of the tree which is represented the by side AB.
and we are given that bases of wires and tree base are at a distance 4 ft.
i.e. side BC = 4 ft
If we look at the [tex]\triangle ABC[/tex], we are given the base BC and the [tex]\angle ACB[/tex], and the perpendicular is to be find out.
We can use trigonometric identity:
[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]
[tex]tan 75^\circ = \dfrac{AB}{BC}\\\bold {tan (45+30)^\circ }= \dfrac{AB}{4}\\\Rightarrow AB = \bold {tan (45+30)^\circ } \times 4 = 14.93\ ft[/tex]
Hence, D. [tex]tan(30^\circ+45^\circ)[/tex] is the correct answer.
