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12. Use a trigonometric ratio to find the measure of O in the triangle below. Give your answer to the nearest degree.

12 Use a trigonometric ratio to find the measure of O in the triangle below Give your answer to the nearest degree class=

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VirαtKσhli

Given :-

  • A right angled triangle with two sides 10cm and 9cm .

To Find :-

  • The value of theta .

Solution :-

At angle theta , 9cm side will be considered as the perpendicular and 10cm side will be hypotenuse . So , as we know that ;

[tex]\longrightarrow sin\theta =\dfrac{perpendicular}{hypotenuse}[/tex]

Substituting the respective values,

[tex]\longrightarrow sin\theta =\dfrac{9cm}{10cm}[/tex]

Simplify,

[tex]\longrightarrow sin\theta= 0.9 [/tex]

Take arcsin both sides ,

[tex]\longrightarrow \theta =sin^{-1}(0.9)[/tex]

[tex]\\\longrightarrow\underline{\underline{\theta = 64.15^o }} [/tex]

Hence the required answer is 64.15° .

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