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Background: I have just about high school knowledge of math, I am sorry if this is a stupid question.

In school, we learned that when transposing, this:

y = x * 3

would become

x = y / 3

I was reading up on trigonometry, and as I was reading the following:

If we look at the general definition -

enter image description here

we see that there are three variables: the measure of the angle x, and the lengths of the two sides (Opposite and Hypotenuse). So if we have any two of them, we can find the third.

In the figure above, click 'reset'. Imagine we didn't know the length of the hypotenuse H. We know that the sine of A (60°) is the opposite side (26) divided by H.

enter image description here

From our calculator we find that sin60 is 0.866, so we can write

enter image description here

Transposing:

enter image description here

which comes out to 30.02

(From http://www.mathopenref.com/sine.html)

As per the rules of transposition (that I probably got wrong), isn't it supposed to read

H = 26 * 0.866

What am I missing?

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We first divide both sides by $H$: $$0.866=\frac{26}{H},$$ then we divide by $0,886$ on both sides: $$0.886H=26,$$ We receive this result: $$H=\frac{26}{0.866}.$$

Thus, the answer is $30.06.$

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Transpose means to isolate the variable. In the problem given you are trying to isolate the $H$ variable. Using algebra:

our problem: $$0.866 = \frac{26}H $$

$$H\cdot 0.866 = \frac{26}H \cdot H$$

$$0.866H = 26$$

$$\frac{0.866H}{0.866} = \frac{26}{0.866}$$

$H = 30.02$ is the correct answer not $30.06$.

Multiplying both sides by $H$ cancels the $H$ in the quotient. Dividing both sides by the coefficient of $H$ cancels the $0.866$ in the product.

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