cosine law distance between houses

Question

Bill and Betty want to calculate the distance between their houses which are opposite sides of a water park.They mark a point,A, 150m along the edge of the water park from Bettys house. The measure of angleNBA as 80 degrees and angleBAN as 75 degrees. Determine the distance between their houses.

Answer 1

In the triangle ABN, NB̂A=80°, BÂN=75°, so BN̂A=180-(75+80)=25°. BA=150m (given).

The Sine Rule can be used to calculate BN (assumed to be the distance between the houses):

BN/sinBAN=BA/sinBNA, BN/sin(75)=150/sin(25), BN=150sin(75)/sin(25)=342.84m.