823 foot ladder is placed against a vertical wall of a building with the bottom of the latter standing on level ground 8 feet from the base of the building how high up the wall does the Ladder reach

Answer 1

Since the ground is level, the angle between the ground and the vertical wall is 90^o. So, a ladder leaning against that wall forms a right triangle with the hypotenuse being the ladder. (The two remaining sides are the formed by the wall and the ground.)

By the Pythagorean Theorem (a² + b² = c²):

8² + b² = 843² <---> 64 + b² = 710,649

Therefore,

b² = 710,649 - 64 = 710,585

and

b = √710,585 ≈ 842.962

So, the ladder is about 843 ft high.

Answer 2

For this problem you may want to use a visual. You will want to use the pathagorean theorem. You ladder is laying up against the wall so this length is going to be your hypotenuse. Just as a reminder the pathagorean theorem is a^2 + b^2 = c^2. You already have your value for a and for c. So you just need to set up the equation to solve for b. I hope this helps. If you have any further questions or you like to set up a session please feel free to send me a message. I am happy to help!