Two extension ladders are leaning at the same angle against a verticl wall. The 3-m ladder reaches 2.4m up the wall. How much farther up the wall does the 8-m ladder reach?
A square has a perimeter of 12 m.how many possible lengths are there for each side? List them and explain your answer
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Two ladders are leaning at the same angle against a vertical wall.
The shorter ladder is 3 m long and it reaches 2.4 m up the wall.
The longer ladder is 8 m long.
How much farther up the wall does the 8 m ladder reach?
To solve this problem, we can use the concept of similar triangles.
First, let's draw a diagram to visualize the situation. We have a vertical wall and two extension ladders leaning at the same angle against the wall. Let's call the length of the first ladder (3 m) L1 and the length of the second ladder (8 m) L2.
Using the concept of similar triangles, we know that the ratios of corresponding sides of similar triangles are equal.
In this case, the corresponding sides are the height the ladders reach on the wall and the lengths of the ladders. Let's call the height the 3-m ladder reaches H1 and the height the 8-m ladder reaches H2.
We are given that the 3-m ladder reaches 2.4 m up the wall, so H1 = 2.4 m.
Using the ratios of the corresponding sides, we can set up the following equation:
H1 / L1 = H2 / L2
Substituting the given values, we get:
2.4 m / 3 m = H2 / 8 m
To find H2, we can rearrange the equation:
H2 = (2.4 m / 3 m) * 8 m
H2 = 6.4 m
Therefore, the 8-m ladder reaches 6.4 m up the wall.
To summarize:
The 3-m ladder reaches 2.4 m up the wall, and the 8-m ladder reaches 6.4 m up the wall.
You can make a proportion out of this.
(2.4/3) = (x/8)
Solve for x.
If you are to use trig, then
cos angle = 2.4/3, solve for angle.
and cos angle = x/8
solve for x.