Question 28995: If i have a retangle with 20 in diagonal with 30 degree on on sid what is the lenght and width of that retangle?
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! If i have a retangle with 20 in diagonal with 30 degree on on sid what is the lenght and width of that retangle?
I am sorry I am not able to bring my diagram over to the answer box here.
Please do as directed.
Draw a rough sketch of a rectangle.Mark it ABCD,with A as the left hand bottom corner vertex and then naming in order the other three vertices in the anti-clockwise direction.
Markdiagonal DB=20 and mark angle DBA = 30 degrees.
Concentrate your attention on the right angled triangle DAB.
Mark length AB = a and width AD =b
We have angle DAB=90 degrees,the acute angle DBA = 30 degrees.
and the hypotenuse DB=20
Using Pytho Theorem,we have
AB^2+DA^2= DB^2
a^2+b^2=20^2
a^2+b^2=400 ----(1)
Applying the tangent funtion to the angle DBA in this right angled triangle,
we have tan(30)= opp side/adjac side
1/[sqrt(3)] =(b/a)
which gives a =b[rt(3)] ---=-(2)
Using (2) in (1)
a^2+b^2=400
{b[rt(3)]}^2 + b^2 = 400
3b^2+b^2=400
4b^2=400
b^2=100 (dividing by 4)
b= 10
(taking only the positive sqrt as we are talking about sides of a rectangle)
Putting b=10 in (2),we have a =b[rt(3)]= 10[sqrt(3)]
Answer:Length of the rectangle = 10[sqrt(3)] and width = 10
Verification: we should get (length)^2+(width)^2 = (diagonal)^2
LHS= (length)^2+(width)^2
= {10[sqrt(3)]}^2 + 10^2 = (100X3) +100 = 400 = diagonal^2
Therefore our values are correct.
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