The vertical height of the blimp above the ground, which is seen by Jay and Libby while working outside, is 7027 ft.
What is right angle triangle property?
In a right angle triangle, the ratio of the opposite side to the adjacent side is equal the tangent angle between the adjacent side and hypotenuse side.
[tex]\tan\theta=\dfrac{b}{a}[/tex]
Here, (a) is the adjacent side, (b) is the opposite side.
Let the height of the blimp from the ground is y ft and the length of the ground to the Libby's position is x ft shown in the attached image below.
As the angle made by the Libby at the height of the blimp is 43 degrees. Therefore,
[tex]\tan43=\dfrac{y}{x}\\x=1.0724y[/tex] ......1
Here, Jay is mowing the lawn approximately 2,500 feet (ft) from Libby when they both see the blimp.
Libby looks up from her gardening at an angle of while Jay looks up at an angle of 35 degrees. Therefore,
[tex]\tan35=\dfrac{y}{x+2500}[/tex]
Put the value of x in the above equation from equation one as,
[tex]\tan35=\dfrac{y}{1.0724y+2500}\\0.7002(1.0724y+2500))=y \\y\approx7027 \rm \; ft[/tex]
Hence, the vertical height of the blimp above the ground, which is seen by Jay and Libby while working outside, is 7027 ft.
Learn more about the right angle triangle property here;
https://brainly.com/question/22790996
