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∘.

40
∘
.
The boat is 25.17
25.17
feet above the ocean floor.

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


sin40∘≈0.643
sin
⁡
40
∘
≈
0.643
cos40∘≈0.766
cos
⁡
40
∘
≈
0.766
tan40∘≈0.839
tan
⁡
40
∘
≈
0.839

A triangle matching the description of the text.

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The length of the rope is approximately _[blank]_ feet.

Enter your answer as the number that correctly fills in the blank.

If necessary, round your answer to the nearest whole number, like this: 42

Answer 1

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

The length of the rope between the boat and the dock can be calculated by using trigonometry ratio

Using trigonometry ratio

tan 40 = opp/adj

opp = height of ship from the ocean level

adj = length of the rope from ship to dock

0.839 = 25.17/x

0.839x = 25.17

x = 25.17/0.839

x = 30feet

Therefore, the length of the rope between the boat and the dock is 30feet