What is the measure of ∠F, to the nearest degree?
44°
57°
71°
78°

Answer:
A. [tex]44^{\circ}[/tex]
Step-by-step explanation:
We have been given a triangle FGH, we are asked to find the measure of angle F.
We will use law of cosines to solve our given problem.
[tex]c^2=a^2+b^2-2ab\times \text{cos}(C)[/tex], where, a, b and c are sides of triangle and C is the angle opposite to side c.
Upon substituting our given values in above formula we will get,
[tex]5^2=7^2+6^2-2*7*6\times \text{cos}(F)[/tex]
[tex]25=49+36-84\times \text{cos}(F)[/tex]
[tex]25=85-84\times \text{cos}(F)[/tex]
[tex]25-85=85-85-84\times \text{cos}(F)[/tex]
[tex]-60=-84\times \text{cos}(F)[/tex]
[tex]\frac{-60}{-84}=\frac{-84\times \text{cos}(F)}{-84}[/tex]
[tex]\frac{5}{7}=\text{cos}(F)[/tex]
Now we will use arccos to solve for measure of angle F.
[tex]F=\text{cos}^{-1}(\frac{5}{7})[/tex]
[tex]F=44.415308597^{\circ}\approx 44^{\circ}[/tex]
Therefore, the measure of angle F is 44 degrees and option A is the correct choice.