The problem asks us to find the values of $s$ and $t$ in the given right triangle, using sine and cosine functions, and rounding the answers to the nearest tenth. The hypotenuse is 34, and the angle is $23^\circ$.

1. Problem Description

The problem asks us to find the values of $s$ and $t$ in the given right triangle, using sine and cosine functions, and rounding the answers to the nearest tenth. The hypotenuse is 34, and the angle is $23^\circ$.

2. Solution Steps

First, we want to find the value of $s$. We can use the cosine function since $s$ is adjacent to the given angle $23^\circ$, and 34 is the hypotenuse.

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

$$\cos(23^\circ) = \frac{s}{34}$$

$$s = 34 \cos(23^\circ)$$

$$s \approx 34(0.9205)$$

$$s \approx 31.297$$

Rounding to the nearest tenth gives $s \approx 31.3$.

Next, we want to find the value of $t$. We can use the sine function since $t$ is opposite to the given angle $23^\circ$, and 34 is the hypotenuse.

$$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$

$$\sin(23^\circ) = \frac{t}{34}$$

$$t = 34 \sin(23^\circ)$$

$$t \approx 34(0.3907)$$

$$t \approx 13.2838$$

Rounding to the nearest tenth gives $t \approx 13.3$.

3. Final Answer

$s \approx 31.3$

$t \approx 13.3$