Question

Given the diagram below, what is the measure of theta to the nearest degree?

Answer 1

`\theta\text{ = 23}`

To find the value of theta, we have to use the appropriate trigonometric identity

We have the side facing the right angle, called the hypotenuse

We also have the third not side facing the angle given which is the adjacent

The ratio between the adjacent and the hypotenuse is called the cosine

So, the cosine of the angle is equal to the adjacent sides length divided by the hypotenuse

We have this as;

`\begin{gathered} \cos \theta\text{ = }(60)/(65) \\ \\ \theta\text{ = }\cos ^(-1)(60)/(65) \\ =\text{ 23} \end{gathered}`