Question

find the largest angle of △rst.

Explanation:

Step1: Recall angle - side relationship

In a triangle, the largest angle is opposite the longest side. Here, the longest side of $\triangle{RST}$ is $RT = 44$ cm. The angle opposite side $RT$ is $\angle{S}$. We use the Law of Cosines to find $\angle{S}$. The Law of Cosines formula is $c^{2}=a^{2}+b^{2}-2ab\cos{C}$, where $c$ is the side opposite the angle $C$, and $a$ and $b$ are the other two sides.
Let $a = 29$, $b = 41$, and $c = 44$. Then $44^{2}=29^{2}+41^{2}-2\times29\times41\times\cos{S}$.

Step2: Expand the equation

$1936=841 + 1681-2378\cos{S}$.
$1936=2522-2378\cos{S}$.

Step3: Solve for $\cos{S}$

First, rearrange the equation:
$2378\cos{S}=2522 - 1936$.
$2378\cos{S}=586$.
$\cos{S}=\frac{586}{2378}\approx0.2464$.

Step4: Find the angle

$S=\cos^{-1}(0.2464)\approx75.7^{\circ}$.

Answer:

$\angle{S}$