Question

From her window, Carmella looks up to the top of a neighboring building at an angle of 46°. Her
angle of depression to the bottom of the building is 25°
The neighboring building is 180 feet away from the building Carmella is in.
How tall is the neighboring building?
round your answer to the nearest tenth of a foot

Answer 1

Answer:

$270.3\ ft$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the right triangle ADE

Find the value of h1

See the attached figure

h1=AD

$tan(25\°)=\frac{h_1}{180}$

Solve for h1

$h_1=(180)tan(25\°)\\h_1=83.94\ ft$

step 2

In the right triangle ABC

Find the value of h2

See the attached figure

h2=BC

$tan(46\°)=\frac{h_2}{180}$

Solve for h2

$h_2=(180)tan(46\°)\\h_2=186.40\ ft$

step 3

Find the height of the neighboring building

we know that

The height of the neighboring building is equal to

$h=h_1+h_2$

substitute the values

$h=83.94+186.40=270.34\ ft$

Round to the nearest tenth of a foot

$h=270.3\ ft$