The ladders shown below are standing against the wall at the same angle. How high up the wall does the
longer ladder go? (All measurements are in feet.)
ladder measurements: first ladder: 30 ft, ? ft, ? ft
second ladder: 24 ft, 10 ft, ? ft
A. 26 ft B. 14 ft C. 12.5 ft D. 11.25 ft
x/10 = 30/24
x = 12.5
To find the height that the longer ladder goes up the wall, we can set up a proportion using the ratios of the corresponding sides of the similar right triangles formed by the ladders and the wall.
Let's compare the first ladder and the second ladder:
First ladder: 30 ft, ? ft, ? ft
Second ladder: 24 ft, 10 ft, ? ft
The ratio of the lengths of the wall segments will be the same for both ladders. So we can set up the following proportion:
30 ft / ? ft = 24 ft / 10 ft
To solve for the missing length of the first ladder, we can cross-multiply:
24 ft * ? ft = 30 ft * 10 ft
Now we can solve for ? ft:
? ft = (30 ft * 10 ft) / 24 ft
? ft = 300 ft / 24 ft
? ft = 12.5 ft
So, the missing length of the first ladder is 12.5 ft.
Therefore, the longer ladder goes up the wall 12.5 ft high.
The correct answer is C. 12.5 ft.
To find the height on the wall that the longer ladder goes up, we need to use the concept of similar triangles. Similar triangles have proportional sides.
First, let's label the lengths of the ladders and the height on the wall:
ladder measurements: first ladder: 30 ft, ? ft, ? ft
second ladder: 24 ft, 10 ft, ? ft
Let's call the height on the wall for the first ladder as h1 and for the second ladder as h2.
Now, we can set up the proportion:
h1/30 = h2/24
To solve for h2, we need to rearrange the proportion:
h2 = (h1 * 24)/30
Now, let's substitute the answer choices to find the possible heights h2:
A. 26 ft: h2 = (h1 * 24)/30 = (26 * 24)/30 = 20.8 ft
B. 14 ft: h2 = (h1 * 24)/30 = (14 * 24)/30 = 11.2 ft
C. 12.5 ft: h2 = (h1 * 24)/30 = (12.5 * 24)/30 = 10 ft
D. 11.25 ft: h2 = (h1 * 24)/30 = (11.25 * 24)/30 = 9 ft
From the given answer choices, the height on the wall that the longer ladder goes up is 12.5 ft (option C).
0
A squared + B squared = C squared
75 degree angle (4:1)
A = 24 B = 24/4 = 6
576 + 36 = 612
Square root of 612 = 24.74
24.74 + 3 = 27.74
Answer: 26 to 28 foot ladder will be fine for this job.
IT is B