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.
First, let's label the points and distances mentioned in the problem:
- Point A is the point 120m along the edge of the water park from Brianna's house.
- B is Brianna's house.
- N is Noah's house.
Now, let's use the law of sines to set up an equation. Let x represent the distance between Noah and Brianna's houses:
sin(<BAN)/120 = sin(<NBA)/x
We know that the measure of <BAN is 70 degrees and the measure of <NBA is 75 degrees, so we can substitute these values into the equation:
sin(70)/120 = sin(75)/x
To solve for x, we can rearrange the equation and solve for x:
x = (sin(75) * 120) / sin(70)
Now, we can calculate the value of x:
x ≈ (0.9659 * 120) / 0.9397
x ≈ 123.14 meters
Therefore, the distance between Noah and Brianna's houses is approximately 123.14 meters.