Answer:
≈ 18.8 cm
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
The central angle is equal to the arc subtending it, that is 60°
arc = 2πr ×
= 2π × 18 ×
= 36π ×
= 6π ≈ 18.8 cm ( to 1 dec. place )
Answer: the distance of the boat from the foot of the lighthouse is 290.5 feet.
Step-by-step explanation:
The right angle triangle ABC representing the scenario is shown in the attached photo.
Angle A is alternate to the angle of depression, hence, they are the same.
The height of the lighthouse represents the opposite side of the right angle triangle. The distance, x of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.
To determine x, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 11.1 = 57/x
x = 57/Tan 11.1 = 57/0.1962
x = 290.5 feet to the nearest tenth.
