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Determine the value of x.
Question 11 options:

A)

5

B)

5

C)

10

D)



Determine The Value Of X Question 11 Options A 5 B 5 C 10 D class=

Sagot :

Answer:   [tex]\frac{10}{\sqrt{3}}[/tex]

This is equivalent to [tex]\frac{10\sqrt{3}}{3}[/tex]

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Explanation:

To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.

This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.

The expression [tex]\frac{10}{\sqrt{3}}[/tex] is the same as [tex]\frac{10\sqrt{3}}{3}[/tex] after we multiply top and bottom by sqrt(3) to rationalize the denominator.

Side notes:

  • This entire process only applies to 30-60-90 triangles.
  • The hypotenuse of a 30-60-90 triangle is twice as long as the short leg, so the hypotenuse is [tex]2x = 2*\frac{10\sqrt{3}}{3} = \frac{20\sqrt{3}}{3}[/tex]  units long.
  • You could use the tangent ratio to help isolate x. You would either say tan(30) = x/10 or tan(60) = 10/x as the first equation to set up.
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