Question

the set designer for a play painted some background scenery on a large piece of plywood. he used a 13 - foot - long pole to hold the piece of plywood upright, as shown in the diagram below. what is h, the total height in feet of the piece of plywood? feet

Explanation:

Step1: Apply Pythagorean theorem

Let the vertical part of the triangle formed by the pole and the ground be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 13$ (length of the pole) and $b = 5$ (distance on the ground). So $x=\sqrt{13^{2}-5^{2}}$.

Step2: Calculate $x$

$x=\sqrt{169 - 25}=\sqrt{144}=12$.

Step3: Find total height $h$

The total height $h$ of the plywood is the sum of $x$ and the extra 2 - foot part on top. So $h=x + 2$.

Step4: Calculate $h$

$h=12+2=14$.

Answer:

14