Help me determine the distance

Question

Noah and brianna want to calculate the distance between their houses which are opposite sides of a water park from briannas house. The measure ∠NBA as 80° and ∠BAN as 75°. Determine the distance between their houses.

Answer 1

With the additional information you included in the comment, that BA = 150 m, we can solve this problem using the Law of Sines.

Law of Sines: sinA/a = sinB/b = sinN/n (it is usually written with a C, but N matches the picture.)

We need one pair of angle and side opposite. We can use n = BA = 150, and m∠N = 180 - 80 - 75 = 25º.

We are looking for b in this problem.

sinB/b = sinN/n

sin(80º)/b = sin(25º)/150 Cross multiply and then divide to find b.

b = 150sin(80º)/sin(25º) ≈ 350 m

Hope this helps!