Answer: The building is 316.1 feet tall
Step-by-step explanation: Please refer to the attached diagram for details.
Based on the information provided, Neta is at point W, and looks at the top of a building from an angle of elevation measuring 56 degrees and then looks down to the bottom of the building at an angle of depression measuring 32 degrees. The top of the building is point T while the bottom is point B. A line separating angles 56 and 32 is drawn to point M along the line TB. So we now have two right angled triangles, WTM and WBM. In effect, the length of the building which is line TB has been divided into lines x and y.
From triangle WTM, using angle 56 as the reference angle, we calculate x as;
TanW = opposite/adjacent
Tan56 = x/150
By cross multiplication we now have
Tan56 (150) = x
1.4825 (150) = x
x = 222.375
Also, from triangle WBM, using angle 32 as the reference angle, we calculate y as,
TanW = opposite/adjacent
Tan32 = y/150
By cross multiplication we now have
Tan32 (150) = y
0.6249 (150) = y
y = 93.735
Therefore the entire length of the building can be derived from x + y
Length = x + y
Length = 222.375 + 93.735
Length = 316.11
To the nearest tenth of a foot, the building is 316.1 feet tall.
The length should be 316.11
[tex]TanW = opposite\div adjacent\\\\Tan56 = x\div 150[/tex]
Now do the cross multiplication
Tan56 (150) = x
1.4825 (150) = x
x = 222.375
Now
[tex]TanW = opposite\div adjacent\\\\Tan32 = y\div 150[/tex]
Now do the cross multiplication
Tan32 (150) = y
0.6249 (150) = y
y = 93.735
Now the entire length of the building is
Length = x + y
= 222.375 + 93.735
= 316.11
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