A camper wants to know the width of a river. From point A, he walks downstream 60 feet to point B and sights a canoe across the river. It is determined that [tex]\alpha[/tex] = 34°. About how wide is the river? A. 34 feet B. 50 feet C. 89 feet D. 40 feet

Hello!The answer is:The correct option is:D. 40 feet.Why?To solve the problem and calculate the width of the river, we need to assume that the distance from A to B and the angle formed between that distance and the distance from A to the other point (C) is equal to 90°, meaning that we are working with a right triangle, also, we need to use the given angle which is equal to 34°. So, to solve the problem we can use the following trigonometric relation:[tex]Tan\alpha =\frac{Opposite}{Adjacent}[/tex]Where,alpha is the given angle, 34°Adjacent is the distance from A to B, which is equal to 60 feet.Opposite is the distance from A to C which is also equal to the width of the river.So, substituting and calculating we have:[tex]Tan(34\°) =\frac{Width}{60ft}[/tex][tex]Width=60ft*Tan(34\°)=60ft*0.67=40.2ft=40ft[/tex]Hence, we have that the correct option is:D. 40 feet.Have a nice day!