A teacher asked Dwayne to find the values of $$x$$ and $$y$$ in the triangles shown. ![](http://admin.getprephub.com/media/editor/t15_20230225221345042650.png) The teacher provided the following information about the triangles: - Triangle $$A B C$$ is similar to triangle $$P Q R$$. - In triangle $$A B C, \cos (C)=0.92$$. Dwayne claims that the value of $$x$$ can be determined but the information provided is not sufficient to find the value of $$y$$. Which statement about Dwayne's claim is accurate?

Given that, Triangle $$A B C$$ is similar to triangle $$P Q R$$ The angle $$C$$ is equal to the angle $$R$$ $$\cos {C}=0.92$$ (given) In triangle $$A B C$$, $$\cos {C}=\frac{x}{20}$$ and $$\cos {R}=\frac{45}{y}=\cos {C}=0.92$$ The correct statement is "His claim is incorrect because $$\cos (C)=\frac{x}{20^{\prime}}, 0.92$$ can be substituted for $$\cos ({C})$$, and since the triangles are similar, this ratio will be the same as $$\frac{45}{y}$$ ".

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A teacher asked Dwayne to find the values of $x$ and $y$ in the triangles shown.

The teacher provided the following information about the triangles:

Triangle $A B C$ is similar to triangle $P Q R$ .
In triangle $A B C, \cos (C)=0.92$ .

Dwayne claims that the value of $x$ can be determined but the information provided is not sufficient to find the value of $y$ .

Which statement about Dwayne’s claim is accurate?

Select all that apply :

His claim is incorrect because $\cos (C)=\frac{x}{20}, 0.92$ can be substituted for $\cos (C)$ , and since the triangles are similar, this ratio will be the same as $\frac{45}{y}$

His claim is correct because $\cos (C)=\frac{20}{x}$ and $0.92$ can be substituted for $\cos (C)$ , but the cosine of angle $R$ is not given for triangle PQR.

His claim is correct because $\cos ({C})=\frac{x}{20}$ and $0.92$ can be substituted for $\cos ({C})$ , but the cosine of angle ${R}$ is not given for triangle $P Q R$ .

His claim is incorrect because $\cos (C)=\frac{20}{x}, 0.92$ can be substituted for $\cos (C)$ , and since the triangles are similar, this ratio will be the same as $\frac{y}{45}$

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