Question
In $\triangle RAT , \angle S =90^{\circ}, \angle T =30^{\circ}, RT =12 cm$ then find RS and ST.
✓
Answer
As, ∠S = 90°, and ∠T = 30° and RT = 12 cm is given.
Clearly, RTS is a 30°-60°-90° triangle.
We know, Property of 30°-60°-90° triangle i.e.
If acute angles of a right angled-triangle are 30° and 60°, then the side opposite
30° angle is half of the hypotenuse and the side opposite to 60° angle is $\frac{\sqrt3}{2}$ times of hypotenuse.
$\Rightarrow RS =\frac{1}{2} \times RT =\frac{1}{2}(12)=6 cm$
And
$ST =\frac{\sqrt{3}}{2} \times RT =\frac{\sqrt{3}}{2} \times 12=6 \sqrt{3} cm$
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