Question

Drag the tiles to the correct boxes to complete the pairs. Based on the diagram, match the trigonometric ratios with the corresponding ratios of the sides of the triangle.

Answer 1

`tanC=(c)/(b),`
`sinB=(b)/(a),`
`tanB=(b)/(c),` and
`cosB =(c)/(a)`

Explanation:

We can use the phrase SOH-CAH-TOA to help us with this problem. SOH-CAH-TOA stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. This phrase helps to remember which sides of a right triangle get divided by which.

First, we'll evaluate
`cosB`. Referencing CAH (Cosine = Adjacent / Hypotenuse), we know that
`cosB` is equal to the length of the adjacent leg to ∠B, which is c, divided by the length of the hypotenuse of the right triangle, which is a. Therefore,
`cosB =(c)/(a)`.

As for
`tanC`, we can refer to TOA (Tangent = Opposite / Adjacent), which means that
`tanC` is equal to the length of the opposite leg to ∠C, which is c, divided by the length of the adjacent leg to ∠C, which is b. Therefore,
`tanC=(c)/(b)`.

As for
`sinB`, we can refer to SOH (Sine = Opposite / Hypotenuse), which means that
`sinB` is equal to the length of the opposite leg to ∠B, which is b, divided by the length of the hypotenuse of the right triangle, which is a. Therefore,
`sinB=(b)/(a)`.

Finally, we'll evaluate
`tanB`. As TOA tells us,
`tanB` is equal to the length of the opposite leg to ∠B, which is b, divided by the adjacent leg to ∠B, which is c. Therefore,
`tanB=(b)/(c)`.

Hope this helps!