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Helga [31]
3 years ago
13

A store charges the same amount for each pair of socks. A customer can buy 3 pairs of socks for $7.80. Henry bought 4 pairs of s

ocks when they were each on sale for 10% off. He also bought a pair of shoelaces. Henry spent a total of $11.58. How much was the pair of shoelaces?
$1.13
$2.22
$2.34
$2.60
Mathematics
1 answer:
JulijaS [17]3 years ago
6 0

Answer: The socks cost 9.36 so the shoe laces would be 2.22

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Answer:

Let a, b, and c be the height, width, and the diagonal of the screen respectively

Since they form a triangle and the angle between a and b is 90 degrees, according to the Pythagorean Theorem a^2 + b^2 = c^2

Let's assume that the aspect ratio is 16:9. Therefore b/a = 16/9

Now we have a system of two equations with two unknowns. We need to express everything in terms of a single unknown, so let's express a in terms of b.

Since, b/a = 16/9, by cross multiplying 16a = 9b. Therefore a=9b/16.

Now we can subsitute 9b/16 for a in the first equation

a^2+b^2=c^2 becomes (9b/16)^2 + b^2 = c^2

Squaring the nominator and the denominator of the fraction yields

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To perform the addition, we need to express b^2 as a fraction with denominator 256 which is 256b^2/256, Now we have

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Cross multiply to get

337b^2 = 256c^2

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b^2=256c^2/337

Take the square root of both sides to get b

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Lots of complicated Pythagorean responses. This is much simpler to answer with Trigonometry.

TLDR; just multiply the diagonal by the following two coefficients, and add the bezel width, to get the width and height:

w = diag x 0.872 + 2 x bw

h = diag x 0.49 + 2 x bw

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Thats all you need to know to do this.

Now here’s the Teig behind it:

First, calculate the angle of the diagonal relative to the base, using tangent, which yields ::

a = tan(9/16)

This will give you an angle of 0.512 radians (or roughly 30 degrees).

Next, calculate the ratio of the height relative to the hypotenuse (the diagonal length) using arc-sine, which yields the relative proportion of opposite length over the hypotenuse for a given angle:

h = asin(0.512)

The result will be roughly h = 0.49, or 49% of the diagonal.

Finally, get the ratio of eidth to hypotenuse using arc-cosine:

w = acos(0.512)

The result is roughly w = 0.872, or 87.2% of the diagonal.

that’s all the math! Enjoy!

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