Answer:
Distance between boat and light house = 134 m
Step-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 ABC
AB= 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
