You can use the law of sines here to find the measure of angle F.
The approximate measure of angle F is given by
Option B : 44. 4°
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{\sin(\angle A)}{a} = \dfrac{\sin(\angle B)}{b} = \dfrac{\sin(\angle C)}{c}[/tex]
Remember that we took [tex]\dfrac{\sin(angle)}{\text{length of side opposite to that angle}}[/tex]
See the figure attached below for reference
Using the law of sines, we get;
[tex]\dfrac{\sin(\angle F)}{|GH|} = \dfrac{\sin(\angle G)}{|FH|} = \dfrac{\sin(\angle H)}{|FG|}\\\\\dfrac{\sin(\angle F)}{28} = \dfrac{\sin(90^\circ)}{40} = \dfrac{\sin(\angle H)}{|FG|}\\[/tex]
First two terms are enough to evaluate the angle F
[tex]\dfrac{\sin(\angle F)}{28} = \dfrac{\sin(90^\circ)}{40} \\\\sin(\angle F) = 28 \times \dfrac{1}{40} = 0.7\\\angle F = arcsin(0.7)\\\\\angle F = 44.427^\circ[/tex]
(i took that value of angle which comes out non negative(because no reason for distinguishing the sign and we take magnitude) and smaller than 90 degrees since the sum of all three angles of a triangle is 180 degrees)
Thus.
The approximate measure of angle F is given by
Option B : 44. 4°
Learn more about law of sines here:
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