The problem describes a kitchen design scenario. The distance between the stove and the sink is 1.3 meters, and the distance between the sink and the refrigerator is 2.2 meters. The angle formed at the sink between the stove and the refrigerator is 31.9 degrees. We want to find the distance between the stove and the refrigerator.

1. Problem Description

The problem describes a kitchen design scenario. The distance between the stove and the sink is 1.3 meters, and the distance between the sink and the refrigerator is 2.2 meters. The angle formed at the sink between the stove and the refrigerator is 31.9 degrees. We want to find the distance between the stove and the refrigerator.

2. Solution Steps

We can use the law of cosines to find the distance between the stove and the refrigerator. Let $a$ be the distance between the stove and the sink, $b$ be the distance between the sink and the refrigerator, and $c$ be the distance between the stove and the refrigerator. Let $\theta$ be the angle at the sink between the stove and the refrigerator.

Then, the law of cosines states:

$c^2 = a^2 + b^2 - 2ab \cos(\theta)$

We are given that $a = 1.3$ meters, $b = 2.2$ meters, and $\theta = 31.9$ degrees.

Plugging in the values:

$c^2 = (1.3)^2 + (2.2)^2 - 2(1.3)(2.2) \cos(31.9^{\circ})$

$c^2 = 1.69 + 4.84 - 5.72 \cos(31.9^{\circ})$

$c^2 = 6.53 - 5.72 \times 0.8489$

$c^2 = 6.53 - 4.8555$

$c^2 = 1.6745$

$c = \sqrt{1.6745}$

$c \approx 1.294$

3. Final Answer

The distance between the stove and the refrigerator is approximately 1.294 meters.