Question

In $\triangle RST$, $\angle S = 90^\circ$, $\angle T = 30^\circ$, and $RT = 12$ cm, then find $RS$.

Hint:

In a 30°–60°–90° triangle, the hypotenuse is twice the side opposite the 30° angle.

Answer 1

Step 1: Understanding the triangle.
In $\triangle RST$, $\angle S = 90^\circ$ and $\angle T = 30^\circ$. Therefore, it is a 30°–60°–90° right triangle.
Step 2: Property of 30°–60°–90° triangle.
In a 30°–60°–90° triangle, the ratio of sides is given by:
\[ 1 : \sqrt{3} : 2 \] where the side opposite 30° is the smallest, and the hypotenuse is twice that side.
Step 3: Identify the sides.
Given that $RT = 12$ cm (hypotenuse), so the side opposite the 30° angle ($RS$) is half the hypotenuse.
\[ RS = \dfrac{1}{2} \times RT = \dfrac{1}{2} \times 12 = 6 \, \text{cm} \]
Step 4: Conclusion.
Hence, $RS = 6$ cm.
Correct Answer: $RS = 6$ cm