Answer:
53.2 feet
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC
[tex]tan(50^o)=\frac{AC}{BC}[/tex] -----> by TOA (opposite side divided by the adjacent side)
substitute the values
[tex]tan(50^o)=\frac{h}{40}[/tex]
solve for h
[tex]h=(40)tan(50^o)[/tex]
[tex]h=47.7\ ft[/tex]
therefore
The height of the pole is
[tex]h+5.5=47.7+5.5=53.2\ ft[/tex]
The height of the flag pole is 53.2-foot and it can be determined by using trigonometric ratio.
Given that,
The angle of elevation from a viewer to the top of a flagpole is 50°.
The viewer is 40 ft away and the viewer's eyes are 5.5 ft from the ground.
We have to determine,
How high is the pole to the foot?
According to the question,
Let the hypotenuse of the flagpole be h,
The angle of elevation from a viewer to the top of a flagpole is 50°.
The viewer is 40 ft away and the viewer's eyes are 5.5 ft from the ground.
And the height of the pole is ( h + 5.5)
The angle of the elevation of the flagpole is given by,
[tex]\rm Tan\theta = \dfrac{Perpendicular}{Base}[/tex]
Substitute all the values in the formula
[tex]\rm Tan\theta = \dfrac{Perpendicular}{Base}\\\\\rm Tan50= \dfrac{h}{40}\\\\h = tan50 \times 40\\\\h = 1.19 \times 40\\\\h = 47.67 \ feet[/tex]
Therefore,
The height of the flagpole is,
[tex]\rm = h + 5.5\\\\= 47.67 + 5.5\\\\= 53.2 \ feet[/tex]
Hence, The required height of the flag pole is 53.2-foot.
To know more about Trigonometry click the link given below.
https://brainly.com/question/13710437
