Question

In the figure below ABC ~ YZX.Fund tanY, cosY, and sinY.Round your answers to the nearest hundredth.I’m super confused so please help.

Answer 1

We know that the given triangles are similar. That means Angles Y and B are congruent. So, our job is to find Angle B first using trigonometric reasons. Let's use the tangent which is equal to the ratio between the opposite leg and the adjacent leg to angle B

`\begin{gathered} \text{tan(B)=}(14.7)/(14)=1.05=\tan Y \\ B=\tan ^(-1)(1.05)\approx46.4 \end{gathered}`

Which means angle Y is also 46.4°, approximately. Also, the tangent of Y is 1.05 too, because Y and B are congruent. Now, let's find the sine and cosine of B or Y (remember they are equal).

`\sin B=(14.7)/(20.3)\approx0.72=\sin Y`
`\cos B=(14)/(20.3)\approx0.69=\cos Y`

Therefore, the tanY is 1.05, sinY is 0.72 and cosY 0.69.