UDD Question 6 10 pts Solve for x. Round to the nearest tenth (one decimal place). Just type the number, no unit of measurement.

Question

2 years ago

6

G X 240 DI F 48 Next * Previous

1 answer:

NISA [10] · Answer 1 · 2022-12-13T00:46:49+03:00

Answer:

The answer is;

54.4

Step-by-step explanation:

The given parameter are;

Triangle ΔFGH = Right triangle

The length of segment $\overline {FH}$ = 48

The measure of ∠HFG = 28°

The measurement required = The measure of segment $\overline {FG}$ = x

The measure of ∠FHG = 90° angle opposite hypotenuse side of a right triangle

Therefore, ∠FGH = 180° - ∠HFG - ∠FHG = 180° - 90° - 28° = 62°

∠FGH = 62°

By sine rule, we have;

$\overline {FH}$ /(sin ∠FGH) = $\overline {FG}$ /(sin(∠FHG)

By substituting the known values, we have;

48/(sin 62°) = x/(sin(90°)

sin(90°) = 1, therefore, we have;

x/1 = x = 48/(sin 62°) = 54.4 (by rounding the answer to the nearest tenth)

x = 54.4