Question

Jill is standing at the base of her apartment building. She measures the angle of elevation to the top of a nearby tower to be 40º. Then Jill goes to the roof of her apartment building, directly above her previous position, and measures the angle of elevation to the top of the same tower to be 30°. If the height of the tower is 100 meters, the height of Jill's apartment building is meters. NextReset

Answer 1

The distance to the base of the tower is 
tan 40=100/x

x=100/tan 40=119.18 m
from the top of the building, we know the adjacent side but not the opposite
tan 30=opposite/119.18
opposite is 119.18*tan30=68.81 m
The opposite side is the height of the tower ABOVE the apartment building. The tower itself is 100 m high, and the remainder of the height, 31.19 m, is the height of the building.

Answer 2

Answer:

The height of Jill's apartment building is 31.2 m.

Step-by-step explanation:

Consider the figure 1:

The height of the tower is 100 meters.

$tan(\theta) = \frac{opp}{adj}$

She measures the angle of elevation to the top of a nearby tower to be 40º

Therefore, $(\theta)=40^{\circ}$

$\tan(40^{\circ})=\frac{100}{x}$

$x=\frac{100}{tan(40^{\circ})}$

$x=\frac{100}{0.839}$

$x =119.18 m$

Therefore, the length of BC is 119.18 m.

Now, find the length of AE.

$tan(30^{\circ})=\frac{y}{119.18}$

$y=(0.577)(119.18)$

$y=68.8$

Hence, the length of AE is 68.8 m.

Therefore, the height of Jill's apartment building can be calculated as:

100 m-68.8 m = 31.2 m

Hence, the height of Jill's apartment building is 31.2 m.