In a right triangle , if the hypotenuse is four times as long as the perpendicular from the opposite vertex , one of the acute angles is?

- anonymous

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- jhonyy9

can you draw it please ?

- anonymous

pic us not given..

- jhonyy9

indifferent just for what is your oppinion from this pic

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## More answers

- anonymous

|dw:1339328315880:dw| i gues its like dis

- apoorvk

|dw:1339328315376:dw|

- anonymous

my ans is theta=cos-1(1/4)

- apoorvk

@heena - wrong answer. Read the question again.

- anonymous

i did and i dont find any prob as its saying hypotenuse is four times as long as the perpendicular means we cas asume perpendicular as x and hypotenuse as 4x

- anonymous

|dw:1339328062826:dw|
i draw the pic
u can find
ab=4x^2 ---1
and a^2+b^2=16x^2 ----2
and use ab to represent x^2 at equation 2
we can have a^2+b^2=4ab
devide ab two sides, that is
a/b+b/a=4
we can let a/b=tanx (x could be the angle of one of two unknown angles)
so tanx+1/(tanx)=4
let tanx=n
so n+1/n=4, we can rewrite it as n^2-4n+1=0
and \[n=2\pm \sqrt{3}\]
\[\tan x= 2\pm \sqrt{3}\]
and u can work out the value of x that is the angle

- anonymous

The options 60 45 30 15

- anonymous

The correct answer is \(15^\circ \)

- anonymous

@FoolForMath u r correct how????? PLzz show it!

- apoorvk

lol sorry!!
\[tan(15^o) = 2 - \sqrt3\]
and the other angle will automatically be 90-15 = 75 degrees.

- anonymous

Well, I can think of a radical free beautiful solution :)

- anonymous

i did nt understand the method used!

- apoorvk

Don't just think, share it with us. @FoolForMath -_-

- anonymous

@AndrewNJ can u xplain it!

- anonymous

in my answer, the equation 1 ab=4x^2
for area of the triangle equals 0.5ab or 0.5*4x*x

- anonymous

No Idea!

- anonymous

the equation 2, a^2+b^2=4ab
means Pythagorean Theorem

- anonymous

Side a is hypot

- anonymous

ok, dont be serious about a and b which is longer, it doesnt matter
a is perpendicular to b
so 0.5ab is the area of this triangle

- anonymous

and half of hypotenuse times its attitude is also the area of triangle

- anonymous

so these two part, 0.5ab and 0.5*4x*x can be equal

- anonymous

this is the first equation

- anonymous

the second is accroading to Pythagorean Theorem
can u got it?

- anonymous

by the way hypotenuse is the longest side in a right triangle

- anonymous

|dw:1339329313013:dw|
\[\frac{AM}{MB }= \tan \alpha \] \[ \frac{AM}{MC}=\cot \alpha \]
Thus,\[MB+MC =AM(\cot \alpha +\tan \alpha) \]
\[\implies BC = 4AM=2AM \frac{1}{ \sin 2 \alpha}\]
\[\implies \sin 2\alpha =\frac 12 \implies \alpha = 15^\circ \]

- anonymous

@AndrewNJ i have a doubt in ur 1 st eq a^2=4x^2 is that right?

- anonymous

my first eq is 0.5ab=4x^2 !

- anonymous

@FoolForMath yours looks cool!
but i think your method could be a bit difficult

- anonymous

why? I think it's fairly obvious :)

- anonymous

well as far as I'm concerned, i seldom use cot sec :(

- anonymous

high school in my country didnt teach us cot sec,only taught sin cos and tan

- anonymous

which country is that?

- anonymous

guess it!

- anonymous

I am very bad at guessing :(

- anonymous

alright, it's china!

- radar

@AndrewNJ, I am from Missouri, the "show me" state lol, and I would like you to please show me how ab=4x^2 (equation 1 in your first post)

- anonymous

i also want it @AndrewNJ

- anonymous

for 0.5ab is the area of triangle
and 0.5*4x*x is also the area of triangle
so 0.5ab=0.5*4x*x
divide 0.5 in two sides is ab=4x^2

- radar

Thanks, you had already shown that, just that, I was being to dense to see it. Thanks again

- radar

*to too

- anonymous

:)

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