Question

which triangle is similar to △abc if sin(a) = 1/4, cos(a) = √15/4, and tan(a) = 1/√15?

Explanation:

Step1: Recall trig - ratio definitions

$\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(A)=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan(A)=\frac{\text{opposite}}{\text{adjacent}}$. Given $\sin(A)=\frac{1}{4}$, $\cos(A)=\frac{\sqrt{15}}{4}$, then $\tan(A)=\frac{\sin(A)}{\cos(A)}=\frac{1}{\sqrt{15}}$.

Step2: Check ratios in triangles

For similar triangles, corresponding trig - ratios are equal. In $\triangle XYZ$, $\sin(X)=\frac{6}{24}=\frac{1}{4}$, $\cos(X)=\frac{6\sqrt{15}}{24}=\frac{\sqrt{15}}{4}$, $\tan(X)=\frac{6}{6\sqrt{15}}=\frac{1}{\sqrt{15}}$.

Answer:

The triangle similar to $\triangle ABC$ is $\triangle XYZ$.