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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.

In the figure below ABC ~ YZX.Fund tanY, cosY, and sinY.Round your answers to the-example-1
User Dthomasen
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1 Answer

15 votes
15 votes

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.

User Dominic Tracey
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