Question

Little Maggie is walking her dog, Lucy, at a local trail and the dog accidentally falls 150 feet down a ravine! You must calculate how much rope is needed for the repel line. Use the image below to find the length of this repel line using one of the 3 trigonometry ratios taught (sin, cos, tan). Round your answer to the nearest whole number. The repel line will be the diagonal distance from the top of the ravine to Lucy. The anchor and the repel line meet to form angle A which forms a 17° angle. Include all of the following in your work for full credit.

(a) Identify the correct trigonometric ratio to use (1 point)

(b) Correctly set up the trigonometric equation (1 point)

(c) Show all work solving equation and finding the correct length of repel line. (1 point)

Answer 1

(a) The correct trigonometric ratio to use is the tangent ratio (tan).

(b) The trigonometric equation is tan(17°) = Opposite/Adjacent.

(c) tan(17°) = Opposite/Adjacent

tan(17°) = 150/Adjacent

Adjacent = 150/tan(17°)

Adjacent = 150/0.3045