Question

A rope is used to tie a boat to a dock. The angle of depression from the boat to the ocean floor directly beneath the dock is 40°. The boat is 25.17 feet above the ocean floor.

What is the length of the rope between the boat and the dock?

Answer 1

Answer:The length of the rope between the boat and the dock is 30 feet.

What are trigonometric ratios?

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, a rope is used to tie a boat to a dock.

The boat is 25.17 feet above the ocean floor.

Let the length of rope be x.

So, tanθ= Perpendicular/Base

⇒ tan40°= 25.17/x

⇒ 0.839= 25.17/x

⇒ 0.839x= 25.17

⇒ x= 25.17/0.839

⇒ x= 30 feet

Therefore, the length of the rope is 30 feet.

Explanation: