Question

Z 2 cm Given that the two right-angled triangles are 1 similar, for the smaller triangle sin 0 What 2 is the trigonometric ratio of sin 0 of the larger triangle. I em 2 1 1 2 I 2

Answer 1

Given that triangles ABC and XYZ are similar

Step 1 : State the theorem for similar triangles

Side-Side-Side

Thus

$\begin{gathered} AC\cong XZ \\ AB\cong XY \\ BC\cong YZ \end{gathered}$

Step 2: define the sine of the acute angle in the two triangles

$\begin{gathered} In\text{ triangle ABC} \\ \sin \theta=\frac{BC}{AC}=\frac{1}{2} \\ \text{From similarity of the sides} \\ In\text{ triangle XYZ} \\ \sin \theta=\frac{YZ}{ZX}=\frac{1}{2} \end{gathered}$

The answer is 1/2