Answer: The correct option is (A) 67.
Step-by-step explanation: We are given to find the measurement of angle F to the nearest degree.
From the figure, we note that
Triangle FGH is aright-angled triangle with FH as the hypotenuse, where
FG = 5 units, GH = 12 units and FH = 13 units.
m∠F = ?
With respect to angle F, GH is the perpendicular and FG is the base.
From trigonometric ratios, we have
[tex]\sin m\angle F=\dfrac{perpendicular}{hypotenuse}\\\\\\ \Rightarrow \sin m\angle F=\dfrac{GH}{FH}\\\\\\\Rightarrow \sin m\angle F=\dfrac{12}{13}\\\\\\\Rightarrow \sin m\angle F=0.92307\\\\\Rightarrow m\angle F=sin^{-1}(0.92307)\\\\\Rightarrow m\angle F=67.37^\circ.[/tex]
To the nearest degree, m∠F = 67°.
Thus, the measure of angle F is 67°.
Option (A) is CORRECT.
