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I have a question in which a Right angle triangle is given, one of the angle is 50 degree. Since it is a right angle therefor other two angles are 90degrees and 40degrees.

The perpendicular of this triangle is equal to x, while the base of the triangle is equal to y.

The question is if x/y is greater than 1 or not ?

How come I'd know by just using the variable that if the answer would be greater or less than 1 since there is no other sides are given ?

Here is what the Triangle looks like.

enter image description here

There is no additional data given whatsoever.

Community
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Sufiyan Ghori
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3 Answers3

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${x\over y}=\tan50^\circ$

We know that $f(x)=\tan x$ is an increasing function in $(0,{\pi\over2})$

since $50^\circ >{\pi\over4}$

$\therefore \tan{50^\circ}>1$, Hence $({x\over y})>1$

Ruddie
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What are the angles in a right, isosceles triangle? What is the ratio between the two cateta? What happens to the angles when you increase one side? What happens to the ratio?

Emanuele Paolini
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If you want to know if $\frac{x}{y}$ is greater than $1$, you're essentially asking which is greater, $x$ or $y$. If $x>y$, then $\frac{x}{y}>1$ and if $x<y$, then $\frac{x}{y}<1$. (We're talking about an actual triangle here, so both $x$ and $y$ are positively greater than $0$).

Now let's look at the special case where both sides are exactly equal, or $x=y$. (This is called an isosceles triangle). What would that mean for the angles?
To change those angles from those values to the ones you found, which side has to grow, $x$ or $y$? What does that mean for $\frac{x}{y}$?

SQB
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