we know that
If the triangle has a [tex]30[/tex] degree angle and a [tex]60[/tex] degree angle, then the third angle is a [tex]90[/tex] degree angle
so
is a right triangle
[tex]Sin(30\°)=Cos(60\°)=\frac{1}{2}[/tex]
[tex]Cos(30\°)=Sin(60\°)=\frac{\sqrt{3}}{2}[/tex]
Statements
A. The second-longest side is twice as long as the shortest side.
we know that
the ratio between the second-longest side and the shortest side is
[tex]\frac{\sqrt{3}}{1}[/tex]
therefore
the statement A is False
B. The longest side is twice as long as the shortest side
we know that
the ratio between the longest side and the shortest side is
[tex]\frac{2}{1}[/tex]
therefore
the statement B is True
C. Two sides of the triangle have the same length
The statement C is False, because is not an isosceles triangle (45-90-45)
D. The longest side is square root 3 times as long as the shorted side
we know that
the ratio between the longest side and the shortest side is
[tex]\frac{2}{1}[/tex]
The longest side is twice as long as the shortest side
therefore
The statement case D is False
the answer is the option
B. The longest side is twice as long as the shortest side
The correct statement is :
(B) The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given information:
A triangle has a [tex]30^o[/tex] and a [tex]60^o[/tex] angle
Now , the third angle will be [tex]90^o[/tex] angle.
So, it is a right angle triangle:
[tex]sin (30^o)=cos(60^o)=1/2\\cos (306o)=sin (60^o)=\sqrt{3}/2[/tex]
Now, check the statements:
(A)The second longest side is twice as long as the shortest side
We, know that
The ratio between the second longest side and the longest side is [tex]\sqrt{3} /1[/tex]
Hence, the statement is false.
(B)The longest side is twice as long as the shortest side
As we know
The ratio between the longest side and shortest side is 2/1
Hence, the statement is true.
(C)Two sides of triangles have same length
The triangle give is not an isosceles triangle
So, the statement is false.
(D)The longest side is [tex]\sqrt{3}[/tex] times the shortest side:
The ratio between the longest side and shortest side is 2.
Hence , the statement is false.
Hence the correct statement is :
(B) The longest side is twice as long as the shortest side.
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