Use the image below to answer the following question:
1 answer:
Answer: The ratios are both identical. (Choice A)
Why does this answer work?
Well let's refer to the diagram below.
Angle x has side 12 opposite it and the hypotenuse is 13.
This means sin(x) = opposite/hypotenuse = 12/13
Also, angle y has side 12 adjacent to it, meaning,
cos(y) = adjacent/hypotenuse = 12/13
Both trig ratios result in 12/13 and we can say sin(x) = cos(y)
One last thing to notice is that x+y = 90
In other words, if x+y = 90, then sin(x) = cos(y)
Phrased a slightly different way: if x+y = 90, then sin(y) = cos(x)
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Let's start with what we know:
Smaller canvas:
Length (
) = 3ft
Width (
) = 5ft
Larger canvas:
Length (
) = ?
Width (
) = 10ft
Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:
So let's plug it all in from above:
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:
Now divide each side by 5 to isolate
The 5s on the right cancel out, leaving us with:
So the length of the larger canvas is 6 ft
Smaller canvas:
Length (
Width (
Larger canvas:
Length (
Width (
Since these are similar rectangles, we can cross-multiply to calculate the missing length. Here's that formula:
So let's plug it all in from above:
Now we cross multiply by multiplying the top-left by the bottom-right and vice versa:
Now divide each side by 5 to isolate
The 5s on the right cancel out, leaving us with:
So the length of the larger canvas is 6 ft