Question

Which triangle is similar to ABC if sin(A) =cos(A) = vs., and tan(A) = VIS?1_JXR3кMол51312V153246V15のS3v15L V6 N12YTN6

Answer 1

Suppose that triangle ABC is a right triangle; therefore, we can use the following trigonometric identities,

`\sin \theta=(O)/(H),\cos \theta=(A)/(H),\tan \theta=(O)/(A)`

Then, in our case,

`\begin{gathered} (1)/(4)=(O)/(H),(A)/(H)=\frac{\sqrt[]{15}}{4},(O)/(A)=\frac{1}{\sqrt[]{15}} \\ \Rightarrow O=1.A=\sqrt[]{15},H=4 \end{gathered}`

In a diagram,

Comparing the ratio of the corresponding sides of triangles ABC and RST

`\begin{gathered} (13)/(4)=3.25 \\ (12)/(1)=12,\frac{12}{\sqrt[]{15}}=3.09833 \end{gathered}`

The ratio between corresponding sides is not constant; thus, triangle RTS is not similar to ABC.

On the other hand, as for triangle KJI

`\begin{gathered} (12)/(4)=3 \\ \frac{3\sqrt[]{15}}{\sqrt[]{15}}=3 \\ (3)/(1)=3 \end{gathered}`

The ratio is constant; therefore, the answer is triangle JKI