I need help with this please

Question

Ji-yoon leaned a 42-foot ladder against the side of a building. The base of the ladder is 2 feet from the base of the building. The top of the ladder is 6 feet from the top of the building. How tall is the building? Provide an answer accurate to the nearest tenth of a foot.

Answer 1

The building, ladder, and ground form a right triangle with hypotenuse equal 42, short leg equal 2 and the long leg unknown. Use the Pythagorean Theorem to find the length of the long leg.

x² + 2² = 42²

Solving that for x gives the height of the building from the ground to the top of the ladder. Add 6 to that result to get the total height of the building, then round to the nearest tenth to get the answer in feet..

Answer 2

Hello Lillyana, to solve this problem I would recommend first drawing a diagram so that we can get a visual of what is going on. I would draw a straight vertical line to represent the side of the building, then I would draw the ladder leaning up against the building, creating a right triangle with the building and ground. Since we know the top of the ladder hits 6 feet below the top of the building, make sure your diagram doesn't have the ladder going all the way to the top.

Once you have your diagram drawn, label what you know. The base of the ladder is 2 feet from the base of the building, so label the base of our right triangle 2. The ladder is 42 feet long so label the hypotenuse of the right triangle 42. We don't yet know how high, from the ground, the ladder hits the building so label the remaining side of the triangle X. We also know that there is 6 feet of building above the ladder so label that 6.

Now, that we have our diagram drawn and labeled, let's look back at the question to see what we need to do next. The question asks how tall the building is. From our diagram, we can see that 6 + X will give us the height of the building. That means we need to solve for X for us to get that height.

Let's take a look at the right triangle. We know the length of two sides, the base and the hypotenuse. We can use the pythagorean theorem to solve for the third side. The pythagorean theorem is a² + b² = c² where "c" is the hypotenuse and "a" and "b" are the legs. If we plug in what we know, we get 2² + X² = 42². Now we can solve for X.

2² + X² = 42²

4 + X² = 1764 (simplify squares)

-4 -4

X² = 1760 (subtract 4 from both sides to get X by itself)

X = √1760 (take the square root of both sides)

Now we can add 6 to X to get the hight of the building. 6. + √1760 gives us 47.9523539. We want to round our answer to the nearest tenth of a foot. The tenth place is the first digit to the right of the decimal. We currently have a 9 in the tenth place. The 5 to the right of the 9 tells us that we need to round up. When we round nine tenths up we get ten tenths, and have to carry a 1 to the ones place. 47.9523539 would round to 48.0.

Our final answer should be 48.0 feet.