Given:
In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches.
To find:
The measure of ∠P to the nearest degree.
Solution:
According to the law of cosine:
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
Using law of cosine in triangle NOP, we get
[tex]\cos P=\dfrac{n^2+o^2-p^2}{2no}[/tex]
Putting the given values, we get
[tex]\cos P=\dfrac{(910)^2+(110)^2-(820)^2}{2(910)(110)}[/tex]
[tex]\cos P=\dfrac{828100+12100-672400}{200200}[/tex]
[tex]\cos P=\dfrac{167800}{200200}[/tex]
[tex]\cos P=0.83816[/tex]
Taking cos inverse on both sides, we get
[tex]P=\cos^{-1}(0.83816)[/tex]
[tex]P=(33.05367)^\circ[/tex]
[tex]P\approx 33^\circ[/tex]
Therefore, the measure of ∠P is 33°.
33° is the answer.
kinda in a hurry, but this is the answer to Deltamath
