Question

Match the correct trig ratios with their values below (Make sure your calculator is in degree mode first) sin42 [Choose ] cos58 [ Choose cos88 [ Choose < tan50 [Choose ] > tan20 [Choose ]

Answer 1

Remember that on a right triangle, the trigonometric ratios of a given angle are defined as follows:

`\begin{gathered} \sin \theta=\frac{\text{Side opposed to }\theta}{\text{Hypotenuse}} \\ \cos \theta=\frac{\text{Side adjacent to }\theta}{\text{Hypotenuse}} \\ \tan \theta=\frac{\text{Side opposed to }\theta}{Side\text{ adjacent to }\theta} \end{gathered}`

On the given figure, the side opposite to the angle C has a length of 20, the side adjacent to C has a length of 21, and the hypotenyse has a lenght of 29.

On the other hand, the side opposite to the angle A has a length of 21, the side adjacent to the angle A has a length of 20 and the hypotenuse is the same.

Then:

`\begin{gathered} \sin A=(21)/(29) \\ \cos A=(20)/(29) \\ \tan A=(21)/(20) \\ \sin C=(20)/(29) \\ \cos C=(21)/(29) \\ \tan C=(20)/(21) \end{gathered}`