Two boats start their journey from the same point a and travel along directions ac and ad, as shown below: abc is a right triangle with measure of angle abc equal to 90 degrees and length of ab equal to 100 feet. there is a point c on bd such that measure of angle acb is 60 degrees and measure of angle adc is 30 degrees. what is the distance, cd, between the boats? 284.3 ft 115.5 ft 230.9 ft 173.2 ft

From the definition for the tangent function, you know  ab/bc = tan(60°)  ab/bd = tan(30°)then the unknown leg distances are  bc = ab/tan(60°)  bd = ab/tan(30°)then the distance of interest is  cd = bd - bc  cd = ab/tan(30°) - ab/tan(60°)  cd = ab(1/tan(30°) - 1/tan(60°))you can figure it from this, or you can take it one step farther by recognizing the relationship  tan(x) = 1/tan(90°-x)this gives  cd = ab(tan(60° - tan(30°))  cd = (100 ft)·(√3 - (√3)/3)) = (2/3)100√3  cd ≈ 115.5 ft