Question

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

Answer 1

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 ;

$\longrightarrow sin\theta =\dfrac{perpendicular}{hypotenuse}$

Substituting the respective values,

$\longrightarrow sin\theta =\dfrac{9cm}{10cm}$

Simplify,

$\longrightarrow sin\theta= 0.9$

Take arcsin both sides ,

$\longrightarrow \theta =sin^{-1}(0.9)$

$\\\longrightarrow\underline{\underline{\theta = 64.15^o }}$

Hence the required answer is 64.15° .