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 =(perpendicular)/(hypotenuse)`

Substituting the respective values,

`\longrightarrow sin\theta =(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° .