6.
A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
You are not required to show your work, but the drawing features might help you picture the triangle in this scenario better.
13.4 ft
18.0 ft
14.6 ft
16.5 ft
We can use the Pythagorean theorem to solve this problem. Let's call the distance up the building "x". Then we have:
x^2 + 4^2 = 14^2
Simplifying this expression, we get:
x^2 + 16 = 196
Subtracting 16 from both sides, we get:
x^2 = 180
Taking the square root of both sides (and rounding to the nearest tenth), we get:
x ≈ 13.4 ft
Therefore, the ladder reaches approximately 13.4 feet up the building. The answer is option A.
To determine how far up the building the ladder reaches, we can visualize a right triangle formed by the ladder, the building, and the ground. The ladder acts as the hypotenuse of the triangle, and the vertical distance from the ground to the point where the ladder reaches the building is the height we want to find.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we know the length of the ladder (14 feet) and the distance from the base of the building to the ladder (4 feet). Let's call the height we're trying to find "h."
Using the Pythagorean theorem, we can set up the equation as follows:
14^2 = 4^2 + h^2
Simplifying this equation, we get:
196 = 16 + h^2
Subtracting 16 from both sides:
180 = h^2
Taking the square root of both sides:
√180 = h
Since we are asked to round our answer to the nearest tenth of a foot, we can use a calculator or math software to find that the approximate value of √180 is 13.42. Therefore, the ladder reaches approximately 13.4 feet up the building.
So, the correct answer is 13.4 ft.
To solve this problem, we can use the Pythagorean theorem, which states that for a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, the ladder represents the hypotenuse, the distance from the base of the building to the ladder represents one of the legs, and the distance from the ladder to the top of the building represents the other leg.
Thus, we have the equation:
hypotenuse^2 = leg1^2 + leg2^2
Plugging in the given values:
14^2 = 4^2 + leg2^2
Solving for leg2:
leg2^2 = 14^2 - 4^2
leg2^2 = 196 - 16
leg2^2 = 180
leg2 ≈ √180
leg2 ≈ 13.4 ft
Therefore, the ladder reaches approximately 13.4 feet up the building.