Word problem

Question

Two identical apartment buildings are 60 m apart. From her balcony Alison's measurment of the angle of elevation to the top of the adjacent building is 47D. The angle of depression from Alison's balcony to the base of the adjacent building is 26D. Find the height of the buildings.

Answer 1

Draw two buildings (rectangles) and label the distance between them 60 feet. Draw a horizontal line connecting the middle of the two buildings and let Alison's balcony be at one end of the line. Then from Alison's balcony draw a line to the top of the other building - label the angle 47D. Notice that you have a right triangle, the length of the adjacent side is 6p feet, you have the 47D angle, and if you find the length of the opposite side then you have part of the height of the building. 

 

From Alison's balcony draw a line to the bottom of the next building,label the angle 27D, notice that the bottom triangle is also a right triangle with the length of the adjacent sides 60 feet - and you have the opposite angle and are looking for the length off the opposite side.

 

To find the height of the building, add the lengths of the opposites sides of the two triangles. 

 

Tan x = opp/adj so  opp = adj (tan x)

Use this formula to find the opposite sides of both triangle, and the height will be their sum.

Always draw a picture.