Given:
In ΔDEF, d = 5.3 cm, e = 2.4 cm and f=4.7 cm.
To find:
The measure of ∠F to the nearest 10th of a degree.
Solution:
According to the law of cosine:
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
In ΔDEF,
[tex]\cos F=\dfrac{d^2+e^2-f^2}{2de}[/tex]
Putting the given values d = 5.3, e = 2.4 and f=4.7, we get
[tex]\cos F=\dfrac{(5.3)^2+(2.4)^2-(4.7)^2}{2(5.3)(2.4)}[/tex]
[tex]\cos F=\dfrac{11.76}{25.44}[/tex]
[tex]\cos F=0.46226[/tex]
Taking cos inverse on both sides, we get
[tex]F=\cos^{-1}(0.46226)[/tex]
[tex]F=62.4669^\circ[/tex]
[tex]F\approx 62.5^\circ [/tex]
Therefore, the measure of angle F is 62.5 degrees.
