Question

Grace is standing 14 feet from a lighthouse and Kelly is standing 12 feet from Grace. The angle that Grace looks up to see the top of the lighthouse is 45°. The angle that Kelly looks up to see the top of the lighthouse is y°. Find the height, h, of the lighthouse. Find the angle, rounded to the nearest tenth of a degree, in which Kelly looks up to the top of the lighthouse. To the nearest tenth of a degree, find the value of x° . In two or more sentences, explain your calculations

Answer 1

Grace has a 45 degree upwards angle, then the height of the lighthouse is 14'.

Case A. Kelly is 26 feet from the lighthouse.
The arcTangent of 14/26 is a 28.3 degree angle.

Case B. But if Kelly stood closer to the lighthouse, i.e. 2 feet away, then her angle is arcTangent of 14/2 = 81.9 degrees