Question

name the sides from smallest to largest

1. $rt < st < rs$
2. $rt < rs < st$
3. $rs < st < tr$
4. $st < rt < rs$

in triangle $rst$, $\angle r=70^\circ$, $\angle s=50^\circ$, $\angle t=60^\circ$

Explanation:

Step1: Match sides to opposite angles

• Side $RS$ is opposite $\angle T = 60^\circ$
• Side $ST$ is opposite $\angle R = 70^\circ$
• Side $RT$ is opposite $\angle S = 50^\circ$

Step2: Order angles from smallest to largest

$\angle S < \angle T < \angle R$
$50^\circ < 60^\circ < 70^\circ$

Step3: Order sides by opposite angles

In a triangle, the shortest side is opposite the smallest angle, and the longest side is opposite the largest angle. So:
$RT < RS < ST$

Answer:

RT < RS < ST