Question

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Answer 1

A 16-foot ladder is placed against the side of a building, as shown in Figure 1 below. The bottom of the ladder is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, the ladder is moved 4 feet closer to the base of the building, as shown in Figure 2 below.

To the nearest foot, how much farther up the building does the ladder now reach? Show how you arrived at your answer.

Answer 2

Use the law of sines. Knowing that the ladder forms a right triangle with the building you can solve this equation.

Since you know that the hypotenuse of the triangle (the ladder's length) is 16 feet, and the length of one of the sides is 8 feet you can solve for the other side (how high the ladder reaches). You can then perform this operation again for the second condition. The hypotenuse of the triangle will again be 16 feet, but the lenght of the side will now be 4 feet.

$=theta

1st relationship)

sin(90)/16 = sin($)/8

$=30 degrees

30+x+90=180 the angle opposite how high the ladder reaches is thus 60 degrees

set up the law of sines again.

sin(90)/16 = sin(60)/x

x=13.856 feet

now you have to do this procedure again for the other triangle.

sin(90)/16 = sin($)/4

$=14.47 degrees

90+14.47+x=180 the angle opposite where the ladder reaches is thus 75.53 degrees.

sin(90)/16 = sin(75.53)/x

x=15.492 feet

Now subtract the first height from the second

15.492 - 13.856 = 1.636 feet

Round to the nearest foot

2 feet

So the ladder now reaches 2 feet higher.

Hope this helps!

Answer 3

thanks

Answer 4

No problem!