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Math help?

What's the value of x?

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Answer 1 · 2018-03-24T23:31:55

$x = 4$ $x=4$

Explanation:

In a $30 - 60 - 90$ $30-60-90$ special right triangle:
Side opposite to $30$ $30$ degrees: $x$ $x$
Side opposite to $60$ $60$ degrees: $x \sqrt{3}$ $xsqrt3$
Side opposite to $90$ $90$ degrees: $2 x$ $2x$

So in this case we are given the side opposite to the $60$ $60$ degrees, because the hypotenuse is always the opposite side of $90$ $90$ degrees, and the shortest side is always opposite to the shortest angle so in this case $30$ $30$ degrees:

$x \sqrt{3} = 2 \sqrt{3}$ $xsqrt3=2sqrt3$

Solve for $x$ $x$ which is the shortest side:
$x = 2$ $x=2$

Now solve for the hypotenuse:
$2 x = 2 \cdot 2 = 4$ $2x= 2*2= 4$

Now referring to the 45-45-90 triangle with the knowledge that the hypotenuse of the previous triangle was $4$ $4$ , but the hypotenuse for that triangle is actually a leg of this isosceles right triangle:

An isosceles right triangle, is always a 45-45-90 degrees triangle, therefore:
Side opposite to 90 degrees: $x \sqrt{2}$ $xsqrt2$
Side opposite to 45 degrees: $x$ $x$
Side opposite to 45 degrees: $x$ $x$

Since $x$ $x$ is also side opposite to $45$ $45$ degrees:
$x = 4$ $x=4$

Answer 2 · 2018-03-24T23:45:56

From the right angled triangle RST we have

$sin 60 = \frac{R S}{R T} \Rightarrow R T = \frac{2 \sqrt{3}}{\frac{\sqrt{3}}{2}} \Rightarrow R T = 4$ $sin60=(RS)/(RT)=>RT=(2sqrt3)/(sqrt3/2)=>RT=4$

From the right angled triangle RQT we have

$tan 45 = \frac{R Q}{R T} \Rightarrow R Q = R T \cdot tan 45 = 4 \cdot 1 = 4$ $tan45=(RQ)/(RT)=>RQ=RT*tan45=4*1=4$

Hence $x = R Q = 4$ $x=RQ=4$

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Math help?

What's the value of x?

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