Respuesta :
Given:
In ΔOPQ, p = 180 inches, q = 120 inches and ∠O=171°.
To find:
The length of o, to the nearest inch.
Solution:
According to cosine formula,
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
Using cosine formula in ΔOPQ, we get
[tex]o^2=p^2+q^2-2pq\cos O[/tex]
On substituting the values, we get
[tex]o^2=(180)^2+(120)^2-2(180)(120)\cos (171^\circ)[/tex]
[tex]o^2=32400+14400-43200(-0.9877)[/tex]
[tex]o^2=46800+42668.64[/tex]
[tex]o^2=89468.64[/tex]
Taking square root on both sides.
[tex]o=\sqrt{89468.64}[/tex]
[tex]o=299.113[/tex]
[tex]o\approx 299[/tex]
Therefore, the length of o is about 299 inches.
