The problem asks us to find the value of $\cos R$ in the given right triangle $RST$, rounded to the nearest hundredth. We are given that $RS = 14$ and $RT = 29$.

1. Problem Description

The problem asks us to find the value of $\cos R$ in the given right triangle $RST$, rounded to the nearest hundredth. We are given that $RS = 14$ and $RT = 29$.

2. Solution Steps

We have a right triangle $RST$ with a right angle at $S$. We want to find $\cos R$.

The definition of cosine in a right triangle is:

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

In triangle $RST$, the side adjacent to angle $R$ is $RS$, and the hypotenuse is $RT$. Therefore,

$\cos R = \frac{RS}{RT}$

We are given that $RS = 14$ and $RT = 29$. Substituting these values into the equation:

$\cos R = \frac{14}{29}$

Now we need to calculate the value of $\frac{14}{29}$ and round to the nearest hundredth.

$\frac{14}{29} \approx 0.4827586...$

Rounding to the nearest hundredth (two decimal places), we look at the third decimal place. Since it is 2 (less than 5), we round down.

$\cos R \approx 0.48$

3. Final Answer

0.48