Reflect one of the lines in the vertical segment that represents the street and draw a new segment from the reflected point to the opening of the opposite building.
About 36.4 feet below the art museum. Diagram:
Practice makes perfect
To find the shortest combined distance, we first have to reflect one of the lines in the vertical segment that represents the street.
Next, we will draw a segment from the reflected point to the opening of the library.
Since the triangles have at least two pairs of congruent angles, we know they are similar by the AA Similarity condition. The sides labeled x and 80-x are both the included side to the marked angles in the triangles. Therefore, they are corresponding legs. Using the triangles' similarity, we can write an equation containing x.
80-x/x=60/50
Let's solve this equation for x.
She should park about 36.4 feet below the art museum. Let's show this in a table.
|c|c|c|
x & 80-x & sum of hypotenuses
35.6 & 44.4 & 136.0203
36 & 44 & 136.0159
36.4 & 43.6 & 136.0147
36.8 & 43.2 & 136.0165
As you can see, the sum of the hypotenuses is minimized when x=36.4.
