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Find value of x in the 30° - 60° - 90° triangle. Give your answer as a simplified radical.

Find Value Of X In The 30 60 90 Triangle Give Your Answer As A Simplified Radical class=

Sagot :

VirαtKσhliidn

Given :-

  • A 30° - 60° - 90° traingle is given to us .
  • The perpendicular is 15 units .

To Find :-

  • The value of x .

Answer :-

As we can see that the triangle is divided by perpendicular bisector . So , the base gets divided into two equal halves . Here we will have to use the ratio of tan , as ;

[tex]\sf\longrightarrow[/tex] tan 60° = 15/x

[tex]\sf\longrightarrow[/tex] √3 = 15/x

[tex]\sf\longrightarrow[/tex] x = 15/√3

[tex]\sf\longrightarrow[/tex] x = √3² * 5/√3

[tex]\sf\longrightarrow[/tex] x = 5√3

[tex]\sf\longrightarrow[/tex] x = 5 * 1.732

[tex]\sf\longrightarrow[/tex] x = 8.66

Hence the required answer is 5√3 or 8.66 units.

Mhanifaidn

Answer:

  • x = 5√3

Step-by-step explanation:

The property of 30° - 60° - 90° right triangle, side ratios are:

  • s : l : h = 1 : √3 : 2

Since side x is opposite to 30° angle, it's the short leg and 15 is the long leg. Use ratios to find the value of x:

  • x : 15 = 1 : √3
  • x = 15/√3
  • x = 15√3/3
  • x = 5√3
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