Given:
∠M = 0.775 radians, m = 5 ft, n = 7 ft, p = 4 ft
To find:
The measure of angle P.
Solution:
Using law of cosine:
[tex]p^2=m^2+n^2-2mn \cos P[/tex]
Substitute the given values.
[tex]4^2=5^2+7^2-2\times 5 \times 7 \cos P[/tex]
[tex]16=25+49-70 \cos P[/tex]
[tex]16=74-70 \cos P[/tex]
Subtract 74 from both sides.
[tex]16-74=74-70 \cos P-74[/tex]
[tex]-58=-70 \cos P[/tex]
Multiply by -70 on both sides.
[tex]$ \frac{-58}{-70} =\frac{-70 \cos P}{-70}[/tex]
[tex]$ \frac{29}{35} = \cos P[/tex]
[tex]$\cos^{-1} \frac{29}{35} = P[/tex]
[tex]$34^\circ = P[/tex]
The measure of angle P is 34°.
