Question

Find measurement of F to the nearest degree

Answer 1

Check the picture below

if your calculator is in Degree mode, you'll get the angle in degrees, if in Radian mode, you'll get radians get taking the inverse sine, so you know

Answer 2

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

$\sin m\angle F=\dfrac{perpendicular}{hypotenuse}\\\\\\ \Rightarrow \sin m\angle F=\dfrac{GH}{FH}\\\\\\\Rightarrow \sin m\angle F=\dfrac{12}{13}\\\\\\\Rightarrow \sin m\angle F=0.92307\\\\\Rightarrow m\angle F=sin^{-1}(0.92307)\\\\\Rightarrow m\angle F=67.37^\circ.$

To the nearest degree, m∠F = 67°.

Thus, the measure of angle F is 67°.

Option (A) is CORRECT.