Noah and Brianna want to calculate the distance between their houses which are opposite sides of a water park. They mark a point, A, 120m long the edge of the water park from Brianna's house. The measure <NBA as 75degree and <BAN as 70degree. Determine the distance between their houses.

To determine the distance between Noah and Brianna's houses, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we can set up the following ratios:

sin(BAN) / BA = sin(NBA) / AN

We are given that angle BAN measures 70 degrees, so we can substitute the values:

sin(70) / BA = sin(75) / AN

Next, we can find the value of sin(70) and sin(75). Using a calculator, we obtain:

sin(70) ≈ 0.9397
sin(75) ≈ 0.9659

Substituting these values into the equation, we have:

0.9397 / BA = 0.9659 / AN

Now, to simplify the equation, we can cross-multiply:

0.9397 * AN = 0.9659 * BA

Divide both sides of the equation by 0.9397 to solve for AN:

AN = (0.9659 * BA) / 0.9397

We are given that point A is 120m along the edge of the water park from Brianna's house. Therefore, BA = 120m.

Substituting this value into the equation, we have:

AN = (0.9659 * 120) / 0.9397

Using a calculator to perform the calculation, we get:

AN ≈ 124.1888

Hence, the distance between Noah and Brianna's houses is approximately 124.1888 meters.