honchos wrote:
If in a right-angled triangle, the ratio of the longer leg to the shorter is √2:1, what is the ratio of the shorter leg to the hypotenuse?
A. 1:3
B. 1:√3
C. √2:√3
D. 3:2
E. √3:1
Doubt: Actually the question is pretty straightforward but "leg" is used only for base and height? or we can use the word in question stem for any of the 3 components that makes up for a right angled triangle: Hypotenuse, base, Height.
M23-03
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Since the is a right angled triangle
\({AC}^2\) = \({AB}^2\) + \({BC}^2\)
So, \({AC}^2\) = \({√2}^2\) + \({1}^2\)
Or, \({AC}^2\) = \({2}\) + \({1}\)
Or, \(AC\) = √3
Quote:
Ratio of the shorter leg to the hypotenuse
Will be \(\frac{BC}{AC}\) => 1:√3
Hence answer will be (B) _________________