Answer:
5.5 ft
Step-by-step explanation:
To find the height of flagpole c, we can use similar triangles.
The two flagpoles and their shadows form two right-angled triangles that are similar.
The height of the larger right triangle is a = 13.2 ft, and its base is x + y = 24 ft. The height of the smaller right triangle is c, and its base is y = 10 ft.
The ratios of corresponding sides in similar triangles are equal, meaning the ratio of height to base is given by:
[tex]\dfrac{a}{x + y} = \dfrac{c}{y}[/tex]
Substituting the known values:
[tex]\dfrac{13.2}{24}=\dfrac{c}{10}[/tex]
Multiply both sides of the equation by 10 is isolate c:
[tex]c=\dfrac{13.2}{24}\times 10\\\\\\c=\dfrac{13.2\times 10}{24}\\\\\\c=\dfrac{132}{24}\\\\\\c=5.5[/tex]
Therefore, the height of flagpole c is:
[tex]\LARGE\boxed{\boxed{c=5.5\; \sf ft}}[/tex]
