Respuesta :
Answer: The boat in the water is 137.37≈ 137 feet far away from the base of light house.
Step-by-step explanation:
Since we have given that
Height of lighthouse above sea level = 50 feet
Angle of depression to the boat in the water = 20°
We need to find the distance from the base of the light house to the boat in the water.
So, it will form a right angled triangle:
Here, AB = 50 feet
∠ACB = 20°
So, we will use "Tangent of a triangle ":
[tex]\tan 20^\circ=\dfrac{AB}{BC}\\\\\tan 20^\circ=\dfrac{50}{BC}\\\\BC=\dfrac{50}{\tan 20^\circ}\\\\BC=137.37\ feet[/tex]
Hence, the boat in the water is 137.37≈ 137 feet far away from the base of light house.
