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 $RT = 29$.

GeometryTrigonometryRight TrianglesCosineTriangle Properties
2025/4/1

1. Problem Description

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

2. Solution Steps

We have a right triangle RSTRST with a right angle at SS. We want to find cosR\cos R.
The definition of cosine in a right triangle is:
cos(θ)=adjacenthypotenuse\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
In triangle RSTRST, the side adjacent to angle RR is RSRS, and the hypotenuse is RTRT. Therefore,
cosR=RSRT\cos R = \frac{RS}{RT}
We are given that RS=14RS = 14 and RT=29RT = 29. Substituting these values into the equation:
cosR=1429\cos R = \frac{14}{29}
Now we need to calculate the value of 1429\frac{14}{29} and round to the nearest hundredth.
14290.4827586...\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.
cosR0.48\cos R \approx 0.48

3. Final Answer

0.48

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