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11. Use a trigonometric ratio to find the length of x in the triangle. Give your answer to two decimal places.

11. Use a trigonometric ratio to find the length of x in the triangle. Give your answer to two decimal places. class=

Answer :

VirαtKσhli

Given :-

  • A right angled triangle with two of the sides as x and 9m .
  • One of the acute angle is 28°

To Find :-

  • The value of x .

Solution :-

As we know that in any right angled triangle ,

[tex]\longrightarrow tan\theta = \dfrac{perpendicular}{base}[/tex]

In the given triangle , perpendicular is x and the base is 9m . Substituting the respective values ,

[tex]\longrightarrow tan\theta = \dfrac{x}{9m} [/tex]

Also here ,

[tex]\longrightarrow \theta = 28^o[/tex]

So that ,

[tex]\longrightarrow tan28^o = \dfrac{x}{9m} [/tex]

Substituting the value of tan28° ,

[tex] \longrightarrow 0.53 = \dfrac{x}{9m}[/tex]

Cross multiply ,

[tex]\longrightarrow x = 9m \times 0.53 [/tex]

Multiply the constants ,

[tex]\longrightarrow\underline{\underline{ x = 4.77m }} [/tex]

Hence the value of x is 4.77 m .

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