WPP#12: Unit O Concept 10: Solving Angles of Elevation and Depression Word Problems

Directions: Read the word problem and answer the question.Show all work and steps clearly.

This picture will go over the solution to this word problem.Make sure to try it on your own first before looking at this picture.


Part A:
Scott went to San Francisco to sight see what his friends called the best city in the world! Of course, he wanted to intake the beauty of the city by standing from one of the great buildings. He was approximately 45 ft. from one of the buildings. He measured the elevation to the building to be 25 degrees. He wanted to know how many feet above the ground his view would be. How tall was the building?



Note:  "X" is the missing side that we need, the height of the building (also the opposite side). The distance between Scott and the building is 45 ft, which is adjacent to the angle (elevation). Remember to use tan and not the inverse since we are not looking for an angle, but a side instead.

Part B:
Once he was at the top of the building, he spotted his best friend Anna who happened to be at the ice cream shop eating ice cream. Suddenly, he got a crave for ice cream and wanted to accompany her. The angle of depression from the top of the building to Anna was 29 degrees. How far apart was the building that Scott was standing on to the ice cream shop that Anna was at? (Hint: Use "Part A" to find the length of the building. This will help you complete the ratio.)


Note: Since we referred back to the previous part and found out that "x" (height) was 20.98 ft. we can make that the adjacent side to the ratio. The missing distance between both building is represented by the variable "x", which also tangent. Again, we only use tan and not the inverse since we are only looking for the distance and not the angle.