Answer
10 ft
Work Step by Step
The distance from the swimmer's head to the lifeguard's head represents the hypotenuse of a right triangle. The length of one leg is shown in the figure as 8 ft. The length of the other leg is the difference between the height of the lifeguards head (11 ft) and the height of the swimmer's head (5 ft). Substitute the given values and solve.
$a^2+b^2=c^2 \longrightarrow$ substitute
$8^2+(11-5)^2=c^2 \longrightarrow$ subtract
$8^2+6^2=c^2 \longrightarrow$ find the squares
$64+36=c^2 \longrightarrow$ add
$100=c^2 \longrightarrow$ find the square root of each side
$\sqrt {100}=\sqrt {c^2} \longrightarrow$ simplify
$10=c$
