Question

Triangle G H F is shown. Angle F G H is a right angle. The length of G H is 28 and the length of hypotenuse F H is 40.

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

What is the approximate measure of angle F? Use the law of sines to find the answer.

11.5°
44.4°
68.0°
81.9°

Answer 1

44.4

Explanation:

right on edge

Answer 2

Using the sine rule:

40/sin(90) = 28/sin(x)

These are two fractions that are equal so we can cross multiply to get:

40 x sin(x) = 28 x sin(90)

Rearranging:

sin(x) = (28 x sin(90))/40

Take inverse sine to find x (the angle)

x = sin^-1(28 x sin(90))/40)

X = 44.4° to 1dp

Lmk if anything’s unclear.