In both figures, we have a right triangle formed by the ladder, the building, and the ground.
In Figure 1, the ladder is 16 feet long, and the distance from the base of the building to the ladder (the adjacent side) is 8 feet. We can use the Pythagorean theorem to find the height of the building (the opposite side):
height^2 + 8^2 = 16^2
height^2 = 16^2 - 8^2
height^2 = 192
height ≈ 13.86 feet
So in Figure 1, the ladder reaches a height of about 13.86 feet up the building.
In Figure 2, the ladder is 4 feet closer to the base of the building, so the distance from the base to the ladder is now 4 feet. We can use the same method to find the new height:
height^2 + 4^2 = 16^2
height^2 = 16^2 - 4^2
height^2 = 240
height ≈ 15.49 feet
So in Figure 2, the ladder reaches a height of about 15.49 feet up the building.
To find how much farther up the building the ladder reaches in Figure 2 compared to Figure 1, we can subtract the two heights:
15.49 - 13.86 ≈ 1.63
So to the nearest foot, the ladder now reaches 2 feet farther up the building (since we must round up when the decimal is 0.5 or greater).
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.
Image: www(dot)connexus(dot)com/content/media/464825-4252011-83536-AM-1403738699/res00000/ppg/examview/H_GEOMB_07_02_Honors_Geometry_7B_Unit_Test/es064-1(dot)jpg
To the nearest foot, how much farther up the building does the ladder now reach? Show how you arrived at your answer.
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