you live in the building on the left in the drawing, and a friend lives in the other building. the two of you are having a discussion about the heights of the buildings, and your friend claims that the height of his building is more than 1.50 times the height of yours. to resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of 21° above the horizontal, whereas your line of sight to the base of the other building makes an angle of 52° below the horizontal. determine the ratio of the height of the taller building to the height of the shorter building. state whether your friend is right or wrong.

1.3

Friend is wrong

Step-by-step explanation:

Given:

friend's claim: height of his building is more than 1.50 times the height of yours

line of sight to the top edge of the other building makes an angle of 21° above the horizontal

line of sight to the base of the other building makes an angle of 52° below the horizontal

Solution:

Let A be the height of your building is A

Let B+A his building is B higher than yours.

Let the distance between the buildings is x.  

then

tan 52 = A/x

tan 21 = B/x  

A/B = tan 52 / tan 21

      =  1.27994 / 0.38386

A/B = 3.33

(A + B) / A = 1.5 0

A/A + B/A = 1.50

1 + B/A = 1.50

B/A is basically (B/x) / (A/x)

So

1+ 3.33 / 3.33

= 4.33/3.33

= 1.3

Since 1.3 is not equal to 1.5

Hence the friend's claim is wrong.