Question

question

1. a 35-foot wire is secured from the top of a flagpole to a stake in the ground. if the stake is 14 feet from the base of the flagpole, how tall is the flagpole? round to the nearest hundredth if necessary.

answer attempt 1 out of 10
additional solution no solution

Explanation:

Step1: Define right triangle sides

Let $c=35$ ft (hypotenuse, wire), $b=14$ ft (base, distance to stake), $a$ = flagpole height (unknown leg). Use Pythagorean theorem: $a^2 + b^2 = c^2$

Step2: Rearrange to solve for $a$

Rearrange formula: $a = \sqrt{c^2 - b^2}$

Step3: Substitute values and calculate

$$\begin{align*} a &= \sqrt{35^2 - 14^2}\\ &= \sqrt{1225 - 196}\\ &= \sqrt{1029}\\ &\approx 32.08 \end{align*}$$

Answer:

32.08 ft