Carlos and Jina are standing on a riverbank, 120 meters apart, at points $A$ and $B$ respectively. (See the figure below.) They want to know the distance from Jina to a house located across the river at point $C$. Carlos measures angle $A$ (angle? $B A C$ ) to be $44^{\circ}$, and Jina measures angle $B$ (angle $A B C$ ) to be $64^{\circ}$. What is the distance from Jina to the house? Round your answer to the nearest tenth of a meter.

Step 1 ：Carlos and Jina are standing on a riverbank, 120 meters apart, at points A and B respectively. They want to know the distance from Jina to a house located across the river at point C. Carlos measures angle A (angle BAC) to be 44 degrees, and Jina measures angle B (angle ABC) to be 64 degrees.

Step 2 ：We can use the Law of Sines to solve this problem. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Step 3 ：In this case, we know the length of side AB (120 meters) and the angles at A and B. We can use this information to find the length of side BC, which is the distance from Jina to the house.

Step 4 ：First, we convert the angles from degrees to radians. Angle A is \(44^\circ\) which is approximately 0.767944870877505 radians, and angle B is \(64^\circ\) which is approximately 1.117010721276371 radians.

Step 5 ：Then, we use the Law of Sines to find the length of side BC. The formula is \(BC = \frac{AB \cdot \sin(A)}{\sin(B)}\). Substituting the known values, we get \(BC = \frac{120 \cdot \sin(0.767944870877505)}{\sin(1.117010721276371)}\), which gives us BC = 155.26378165519606 meters.

Step 6 ：Rounding to the nearest tenth of a meter, we get BC = 155.3 meters.

Step 7 ：Final Answer: The distance from Jina to the house is approximately \(\boxed{155.3}\) meters.