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Standing on top of a building, you use a laser measuring tape to measure your distance from the top and bottom of a nearby statue.You notice that you are a=180 feet from the top of the statue and b=212 feet from the bottom of the statue, and that the angle formed between the top and bottom of the statue is θ=22∘.How tall is the statue? feet   

Standing On Top Of A Building You Use A Laser Measuring Tape To Measure Your Distance From The Top And Bottom Of A Nearby StatueYou Notice That You Are A180 Fee class=

Sagot :

Consider the following diagram,

Consider the side 212 feet side makes an angle as denoted in the figure.

Consider that both the triangle have the same base length,

[tex]180\sin (\varnothing+22)=212\sin (\varnothing)\Rightarrow\frac{\sin (\varnothing+22)}{\sin (\varnothing)}=\frac{212}{180}=\frac{53}{45}[/tex]

Solve the expression further,

[tex]\frac{\sin\varnothing.\cos22^{\circ}+\cos\varnothing.\sin22^{\circ}}{\sin\varnothing}=\frac{53}{45}\Rightarrow0.927^{}+\cot \varnothing.(0.3746)=\frac{53}{45}[/tex][tex]0.3746\cot \varnothing=0.251\Rightarrow\cot \varnothing=0.66945\Rightarrow\varnothing\approx56.2^{\circ}[/tex]

Now, the height of the statue is calculated as,

[tex]h=b.\cos \varnothing-a.\cos (\theta+\varnothing)=212.\cos 56.2-180.\cos (22+56.2)=154.744[/tex]

Thus, the height of the statue is approximately 154.744 feet.

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