Answer: 40 ft
Step-by-step explanation:
I would start this problem out by drawing a picture. There is a building involved, so you will draw a right triangle, since the walls of a building and the ground create a 90 degree angle. Remember, the hypotenuse is the longest side and will be across from the right angle.
Start out by drawing a triangle: the building will be the vertical side, the ground will be the horizontal side, and the ladder will be the hypotenuse.
Label your triangle: from the problem, we know that the ladder is 41 feet long, so we can say the hypotenuse is 41. We also know that the base of ladder is 9 feet away from the building, so we can label the horizontal side as 9. We want to find the height of the ladder on the building, so we can label that side as b.
Use the Pythagorean theorem: remember the Pythagorean theorem is [tex]a^2+b^2=c^2[/tex], so we can plug in what we know. The hypotenuse is always c, so we can plug in 41 for c. In this problem, we are calling the base a, so we can plug in 9 for a. That leaves you with the equation [tex]9^2+b^2=41^2[/tex]
Solve: first, square the nine and 41 to get rid of the exponents. That gives us [tex]81+b^2=1681[/tex]. Next, isolate the variable. Subtract 81 from both sides to leave you with [tex]b^2=1600[/tex]. Next, take the square root of both sides. That leaves you with b = 40, which is your answer.
An Easier and Faster Way:
Whenever I get a problem with the hypotenuse and another side, I use the formula [tex]b=\sqrt{c^2-a^2}[/tex] This allows you to do everything in one step and saves more time.
