Answer:
the height of the antenna is 16 ft.
Step-by-step explanation:
Given three sides of the triangles as, 20ft, 20ft, amd 24 ft.
Apply Heroes' formula to determine the area of the triangle;
[tex]s = \frac{20 + 20 + 24}{2} \\\\s = 32\\\\Area = \sqrt{s(s-20)(s-20)(s-24)} \\\\Area = \sqrt{32(32-20)(32-20)(32-24)} \\\\Area = 192 \ ft^2[/tex]
The area of the triangle is also calculated as;
[tex]Area = \frac{1}{2} \times \ base \ \times \ height\\\\A= \frac{1}{2} bh\\\\2A = bh\\\\h = \frac{2A}{b} \\\\h = \frac{2\times 192}{24} \\\\h = 16 \ ft[/tex]
Therefore, the height of the antenna is 16 ft.
