trig problem i need help with

Answer:Distance between boat and light house = 134 mStep-by-step explanation:Given data:Height of light house = 46 m Angle of elevation from boat to the top of light house = 19°From the data given to us we can construct a right triangle ABC.For the Δ ABCAB= 46 m∠C= 19°We can apply trigonometric ratio to find side BC which is the distance of light house from the boat.[tex]\tan19\°=\frac{AB}{BC}[/tex]Multiplying both sides by BC.[tex]BC\tan19\°=\frac{AB}{BC}\times BC[/tex][tex]BC\tan19\°=AB[/tex]Dividing both sides by tan 19°[tex]\frac{BC\tan19\°}{tan 19\°}=\frac{AB}{tan 19\°}[/tex][tex]BC=\frac{AB}{tan 19\°}[/tex]Substituting value of AB and tan 19°[tex]BC=\frac{46}{0.344}[/tex][tex]BC=133.59\ m\approx134\ m[/tex]Distance between boat and light house = 134 m