what is the height of the building?

Question

A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 26.2 degrees. He then moves back 53.9 feet and determines that the angle of elevation is 18.9 degrees. What is the height of the building?

Answer 1

we have two rectangle triangles formed; one has one leg equal to H and the other leg is x the elevation angle of the line from the ground to the top is 26.2 degrees. The other triangle has one leg equal to H and the other leg equal to (X+53.9). We have a common side which is H. So if we make the two H equal we will solve for x

as follows:

Tan 26.2 = (H/x) ; tan 18.9 = (H/(x+53.9), then x *tan 26.2=(x+53.9)*tan 18.9

We have the following equation:

0.4921x = 0.3424x + 18.45

0.1497 x = 18.45 => x= 123.25 feet

The height will be

Tan 26.2=H/123.25 from where H= 60.64feet

Check is:

Tan ^-1( 60.64)/(123.25+53.9) Then angle is 18.9 degrees  OK!!!!!!!!!!!!!!!!!

 

Answer 2

Let x = height of the building 

 

Let y = distance between the bottom of the building & the original angle of elevation 

 

Let y + 53.9 = distance between the bottom of the building & the new angle of elevation

 

Since only the height of the building & the distance on the ground are the only side given, we will use the

 

tangent function.

 

Tan 26.2 = x/y

 

.492 = x/y

 

.492y = x

 

Tan 18.9 = x/(y + 53.9)

 

.3424 = x/(y + 53.9)

 

x = .3424y + 18.4541

 

.492y = .3424y + 18.4541

 

.1496y = 18.4541

 

y = 123.34 feet

 

x = .492 * 123.34 feet = 60.68 feet 

 

The height of the building is 60.68 feet.