Towing A loaded barge is being towed by two tugboats, and the magnitude of the resultant is 6000 pounds directed along the axis of the barge (see figure). Each towline makes an angle of θ degrees with the axis of the barge.(a) Find the tension in the towlines when θ = 20 ∘ .(b) Write the tension T of each line as a function of θ . Determine the domain of the function. (c) Use a graphing utility to complete the table. θ 10∘ 20∘ 30∘ 40∘ 50∘ 60∘ T (d) Use a graphing utility to graph the tension function.(e) Explain why the tension increases as θ increases.Chapter 11, Problem 14PS, Towing A loaded barge is being towed by two tugboats, and the magnitude of the resultant is 6000
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Towing A loaded barge is being towed by two tugboats, and the magnitude of the resultant is 6000 pounds directed along the axis of the barge (see figure). Each towline makes an angle of θ degrees with the axis of the barge.
(a) Find the tension in the towlines when θ = 20 ∘ .
(b) Write the tension T of each line as a function of θ . Determine the domain of the function.
(c) Use a graphing utility to complete the table.
| θ | 10∘ | 20∘ | 30∘ | 40∘ | 50∘ | 60∘ |
| T |
(d) Use a graphing utility to graph the tension function.
(e) Explain why the tension increases as θ increases.
Chapter 11, Problem 14PS, Towing A loaded barge is being towed by two
tugboats, and the magnitude of the resultant is 6000
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