Two buildins are ...?

Question

Two buildings are 31.7 m apart. From the roof of the shorter building the angle of elevation to the top of the taller building is 27 degrees. The angle of depression from the shorter buildin to the base of the taller building is 48 degrees.what is the height of the taller buidling.

Answer 1

A couple of others have done this one, but I'll try it myself and see if I get the same answer. Suppose x is the height of the taller building and y is the height of the shorter. That means x-y is the difference in height.

Using the tangent function, we have

tan 27 = (x-y)/31.7 (Eq 1)
tan 48 = y/31.7 (Eq 2)

From Eq 1, x-y = 31.7 tan 27 ==> x = y + 31.7 tan 27 (Eq 3)
From Eq 2, y = 31.7 tan 48 (Eq 4)

Substitute Eq 4 into Eq 3:

x = 31.7 tan 48 + 31.7 tan 27 = 31.7(tan 48 + tan 27)
x = 51.36 m.

This answer is right. Is it the same as they got?

Answer 2

Assumption, that the two buildings are on the same level ground

Given the angle of depression from the top of the short building to the ground and the distance between them you can calculate the shorter's height.

Hs = 31.7 tan 48 deg

Given the angle of elevation you can calculate how much taller the higher building is

H+ = 31.7 tan 27 deg

so add the two together to get

H = 31.7 (tan 27 deg + tan 48 deg)

Answer 3

If you draw it out, you will get that you will have 2 triangles to work with.

tan(48) = (31.7)/(adjacent)
tan(48) = (31.7)/x
x = (31.7)/(tan(48))

The shorter building is about 28.54 meters tall

tan(27) = opposite/(31.7)
tan(27) = y/(31.7)
y = (31.7)tan(27)

The taller building is about 16.15 meters taller

(31.7)/(tan(48)) + (31.7)tan(27)

The Taller Building is about 44.69 meters tall

Answer 4

51.36m


use Tan 27=h1/31.7

and Tan 48= h2/31.7


solve for h1 and h2 and add them together, giving you the total height h of the building