Emma is walking along the bank of a straight river toward a 20-meter long bridge over the river.(see details)?

Question

(Let X be the angle subtended horizontally by Emma's view of the bridge).

A. Write a formula for Emma's distance from the bridge,d, as a function of X.

B. Write a formula for X as a function of d.

C. Evaluate the formula in part (B) for d = 500, and interpret the result in the context of the problem.

I'm in desperate need of help with this problem. I can't find the position of where Emma is located and need someone to show me how to solve A, B and C in detail.

Answer 1

A) If you draw a picture, you'll get a triangle with angle X, opposite side 20m, and adjacent side d.
Therefore, using SOHCAHTOA, you have the opposite and adjacent sides, so tan X = 20/d. So d = 20/tan X.

B) As before, tan X = 20/d, so X = tan^-1 (20/d).

C) X = tan^-1 (20/500) = 2.29 degrees. So when Emma is 500 m from the bridge, the angle between the ends of the bridge from her point of view is 2.29 degrees.