MHB Find the value of X in terms of Y

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In the discussion, participants focus on finding the value of X in terms of Y using similar triangles. They establish that the ratio of the sides opposite equal angles is consistent, leading to the equation 7/Y = 9/X. This simplifies to 7Y = 9X, confirming the relationship. The final expression derived is X = 7Y/9. Additionally, a note is made about the importance of distinguishing between lowercase and uppercase letters in mathematical notation.
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mathlearn said:
All I see is the three angles of the triangles equal.
In this case the triangles are similar.
 
Evgeny.Makarov said:
In this case the triangles are similar.

As said above,

In similar triangles, the sides facing the equal angles are always in the same ratio

$\frac{7}{X}$ = $\frac{9}{Y}$

$7Y$ = $9X$

Correct I guess?

Many Thanks :)
 
mathlearn said:
$7Y$ = $9X$
Correct, but the final answer is $x=7y/9$ ("find the value of $x$ in terms of $y$").

Also, in mathematics lowercase and uppercase letters often denote different objects, so they should not be mixed.
 
Sure :) Thank you for the advice :)

Many Thanks :)
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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