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.
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.